Permutation and combination
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There are three ways to summarize this document: 1) The document discusses permutations and combinations, explaining how to calculate the number of possible arrangements of people or objects in different scenarios. Formulas are provided such as nPr, nCr, and how they relate to factorials. 2) An example calculates the number of ways to select a team of 5 batsmen, 1 wicketkeeper, 2 spinners, and 3 pacers from groups of 8, 2, 4, and 5 respective people. 3) The last example asks how many ways one player could get all four aces when 52 cards are dealt among 4 players, treating the 4 aces as one card.
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Permutation and combination
1) The document discusses permutations and combinations, which are ways of arranging or selecting items from a group.
2) A permutation is an arrangement of items that considers order, while a combination disregards order.
3) Formulas are provided to calculate the number of permutations and combinations for a given number of items selected from a larger set.
Notes on permutations and combinations
The document defines permutations and combinations. Permutations refer to arrangements where order matters, while combinations refer to selections where order does not matter. Formulas for calculating permutations and combinations are provided. Several examples illustrate calculating the number of possible arrangements and selections in different scenarios involving people, objects, and committees.
permutations power point
Permutations involve arranging objects in a particular order, where order matters. There are a few different formulas to calculate the number of permutations depending on the situation. The basic formula for permutations of n objects taken r at a time is nPr = n!/(n-r)!. Some examples provided calculate the number of permutations when arranging letters, skiers in a competition, and people entering a cave.
Aii12 permutations combinations
This document discusses permutations and combinations. It defines permutations as arrangements that consider order, and combinations as arrangements where order does not matter. Formulas are provided to calculate the number of permutations and combinations of n items taken r at a time. Examples are given to demonstrate calculating permutations and combinations in different scenarios like lock combinations, electing club officers, drawing cards, and selecting test questions.
11.1 combination and permutations
This document discusses permutations and combinations. It provides examples of using formulas and the fundamental counting principle to calculate the number of possible outcomes for different scenarios involving selecting items with or without regard for order. Examples include determining the number of possible sandwiches, voicemail passwords, bead necklace designs, and ways to select people or items from a group. The key concepts of permutations, combinations, and factorials are explained.
Permutation combination
The document defines important terms related to permutation and combination, including factorial, fundamental principle of counting, and different types of permutations and combinations. It provides examples of calculating permutations with and without repetition, as well as combinations with and without repetition. Formulas are given for each case. Permutations refer to arrangements where order matters, while combinations are arrangements where order does not matter.
Permutation and combination - Math Statistic
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and provides an example of finding the number of permutations of selecting 2 letters from a set of 3 letters. Combinations are arrangements where order is not important, and gives an example of finding the number of combinations of selecting 2 letters from a set of 3. It also presents the factorial formulas for permutations and combinations and provides examples of using them to calculate permutation and combination problems. Finally, it highlights the difference between permutations and combinations and provides 4 example problems to practice calculating permutations and combinations.
3. permutation and combination
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and combinations as groupings where order is not important. It provides examples of calculating permutations and combinations using factorial notation and formulas. The differences between permutations and combinations are outlined. Conditions that can be applied, such as objects being together or separated, are also discussed along with how to handle them in calculations.
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Permutation and combination
1) The document discusses permutations and combinations, which are ways of arranging or selecting items from a group.
2) A permutation is an arrangement of items that considers order, while a combination disregards order.
3) Formulas are provided to calculate the number of permutations and combinations for a given number of items selected from a larger set.
Notes on permutations and combinations
The document defines permutations and combinations. Permutations refer to arrangements where order matters, while combinations refer to selections where order does not matter. Formulas for calculating permutations and combinations are provided. Several examples illustrate calculating the number of possible arrangements and selections in different scenarios involving people, objects, and committees.
permutations power point
Permutations involve arranging objects in a particular order, where order matters. There are a few different formulas to calculate the number of permutations depending on the situation. The basic formula for permutations of n objects taken r at a time is nPr = n!/(n-r)!. Some examples provided calculate the number of permutations when arranging letters, skiers in a competition, and people entering a cave.
Aii12 permutations combinations
This document discusses permutations and combinations. It defines permutations as arrangements that consider order, and combinations as arrangements where order does not matter. Formulas are provided to calculate the number of permutations and combinations of n items taken r at a time. Examples are given to demonstrate calculating permutations and combinations in different scenarios like lock combinations, electing club officers, drawing cards, and selecting test questions.
11.1 combination and permutations
This document discusses permutations and combinations. It provides examples of using formulas and the fundamental counting principle to calculate the number of possible outcomes for different scenarios involving selecting items with or without regard for order. Examples include determining the number of possible sandwiches, voicemail passwords, bead necklace designs, and ways to select people or items from a group. The key concepts of permutations, combinations, and factorials are explained.
Permutation combination
The document defines important terms related to permutation and combination, including factorial, fundamental principle of counting, and different types of permutations and combinations. It provides examples of calculating permutations with and without repetition, as well as combinations with and without repetition. Formulas are given for each case. Permutations refer to arrangements where order matters, while combinations are arrangements where order does not matter.
Permutation and combination - Math Statistic
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and provides an example of finding the number of permutations of selecting 2 letters from a set of 3 letters. Combinations are arrangements where order is not important, and gives an example of finding the number of combinations of selecting 2 letters from a set of 3. It also presents the factorial formulas for permutations and combinations and provides examples of using them to calculate permutation and combination problems. Finally, it highlights the difference between permutations and combinations and provides 4 example problems to practice calculating permutations and combinations.
3. permutation and combination
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and combinations as groupings where order is not important. It provides examples of calculating permutations and combinations using factorial notation and formulas. The differences between permutations and combinations are outlined. Conditions that can be applied, such as objects being together or separated, are also discussed along with how to handle them in calculations.
permutation and combination
This document discusses permutations and combinations. It provides examples of using formulas to calculate the number of possible permutations and combinations in different scenarios, such as arranging letters, selecting lock combinations, filling elected offices from a club, being dealt cards in a game, and selecting essay questions from a test. Formulas for permutations and combinations are presented along with step-by-step workings of examples.
PERMUTATION & COMBINATION
This document discusses permutation and combination concepts in counting. It provides examples of using the multiplication principle when order matters and addition principle when order does not matter to count outcomes of events. It also defines permutation as arrangements of objects where order matters and combination as selections of objects where order does not matter. Formulas are given for counting permutations and combinations of distinct objects. Examples demonstrate calculating the number of ways to arrange or select objects in different scenarios.
Permutation and combinations
The document discusses permutations and combinations. It begins by introducing permutations as arrangements of objects in a definite order. It then presents the fundamental principle of counting, which states that if one event can occur in m ways and is followed by another that can occur in n ways, the total number of occurrences is m×n. It provides examples of using this principle to count outcomes. The document then defines permutations more specifically as arrangements of a number of objects taken some or all at a time. It presents a theorem stating the formula to calculate the number of permutations of n distinct objects taken r at a time is nPr = n(n-1)(n-2)...(n-r+1).
Permutations & combinations
The document discusses permutations and combinations. It explains that permutations calculate arrangements where order matters, while combinations calculate arrangements where order does not matter. The fundamental counting principle is introduced as a way to calculate the total number of possible outcomes by multiplying the number of options for each part. An example shows there are 120 ways for 5 students to arrange themselves in 5 consecutive seats, using the fundamental counting principle.
Combinations
The document discusses combinations and restricted combinations. Some key points:
- Combinations refer to the number of ways of selecting items without regard to order, as opposed to permutations which consider order.
- A combination formula is given to calculate the number of combinations of n items taken r at a time.
- Examples demonstrate calculating combinations in situations like selecting committee members or players for a team when certain items must or cannot be included.
- The number of combinations when p particular items must be included is written as n-pCr-p, and when p items cannot be included is n-pCr.
Counting Technique, Permutation, Combination
This document discusses counting techniques including permutations and combinations. It provides examples of using the fundamental counting principle to calculate the number of possible outcomes in situations like selecting shirts from various sizes and colors or generating license plates from letters and numbers. The key concepts of permutations, which involve ordered arrangements, and combinations, which involve unordered selections, are explained along with related formulas. Practice problems apply these techniques to scenarios such as seating arrangements, word rearrangements, and group selections.
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The document discusses permutations and combinations in the context of seating arrangements. It provides examples to determine the number of possible arrangements for seating groups of people. For a group of 3 people, there are 6 possible arrangements. For a group of 5 people, there are 120 possible arrangements, found by multiplying 5 x 4 x 3 x 2 x 1. The document also discusses using permutations and combinations to solve other types of problems involving arrangements and selections where order does or does not matter.
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1. The document contains examples and formulas for permutations and combinations. It discusses linear permutations, distinguishable permutations, circular permutations, and ring permutations.
2. One example asks how many five-letter words can be formed from a set of vowels and consonants if they must alternate with no repetition.
3. The combination formula is presented, and examples ask how to select teams and committees from groups of people.
Permutations and Combinations
This document discusses permutations and combinations. It defines permutations as arrangements that consider order, and combinations as arrangements where order does not matter. The document provides examples of using formulas and the fundamental counting principle to calculate the number of permutations and combinations in different scenarios, such as selecting committees from a group of people or hands of cards from a deck. It emphasizes that there are always fewer combinations than permutations since combinations ignore order.
Permutation
The document discusses permutations and combinations. It defines a permutation as an arrangement of objects where order matters, and a combination as an arrangement where order does not matter. It provides examples of permutations of sets with 3 and 8 elements. The number of permutations of a set of n elements is n factorial. Permutations are arrangements of all elements of a set. The document also provides examples of calculating the number of permutations in different scenarios like seating arrangements and rearrangements of letters in a word.
Permutation and combination
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This document contains 15 multiple choice questions testing concepts in permutations and combinations. Permutations refer to arrangements of distinguishable objects without repetition, while combinations refer to subsets of objects without regard to order. The document also provides examples and formulas for calculating permutations and combinations, including cases where some objects are identical. It defines key permutation terms like factorial and P(n,r) and illustrates their use through examples like finding the number of ways to arrange 5 people for a portrait.
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Permutation and combination
This document discusses permutation and combination. It defines a permutation as an arrangement of objects in a definite order, while a combination is a selection of objects where order does not matter. There are two types of permutations - with and without repetition. The number of permutations of n objects taken r at a time without repetition is nPr = n!/(n-r)!, and with repetition is nr. Combinations can be calculated as nCr = n!/r!(n-r)!. Examples of calculating permutations and combinations in different scenarios are provided.
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This document defines and provides examples of permutations and combinations. Permutations refer to arrangements of objects where order matters, while combinations refer to collections of objects where order does not matter. The key formulas discussed are permutations of n objects taken r at a time (nPr) and combinations of n objects taken r at a time (nCr). Several word problems demonstrate calculating permutations and combinations in different contexts such as arranging letters, selecting teams or committees, and more.
Permutations and combinations
The document discusses various concepts related to permutations and combinations including:
1) It provides examples to explain the difference between permutations and combinations.
2) It lists the formula for permutations as Npr = n! / (n-r)! and provides an example calculation.
3) It poses several word problems involving permutations and combinations and shows the calculations to arrive at the answers.
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This document discusses principles of counting including factorial notation, the fundamental counting principle, permutations, and combinations. Factorial notation (n!) represents the product of all positive integers less than or equal to n. The fundamental counting principle states that if an activity can be completed in n1 ways and another in n2 ways, they can be completed together in n1*n2 ways. Permutations refer to arrangements of objects that consider order, while combinations only consider groupings without order. Formulas to calculate permutations and combinations are provided along with examples of problems applying these principles.
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permutation & combination
shortcut method of permutation and combination. calculate without formula. The study of permutations and combinations is concerned with determining the number of different ways of arranging and selecting objects out of a given number of objects without actually listing them. There are some basic counting techniques which will be useful in determining the number of different ways of arranging or selecting objects. The two basic counting principle are given below:
Countingprinciple
This document discusses counting principles such as the sample space, fundamental counting principle, permutations, and combinations. It defines permutations as ordered arrangements and combinations as non-ordered arrangements. Permutations and combinations are two important counting principles used to calculate the number of possible outcomes.
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Miku wakes up at 6 AM, eats breakfast at 6:20 AM, and leaves for school at 7:30 AM where her day consists of classes, a break for eating at 9:30 AM, more classes, and going home at 12:00 PM. After arriving home, Miku takes a nap, plays soccer, does homework and writes songs from around 6-8 PM, practices dancing at 8 PM, eats dinner at 9:30 PM, and goes to sleep at 12:00 AM, completing her daily routine.
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This document discusses permutation and combination concepts in counting. It provides examples of using the multiplication principle when order matters and addition principle when order does not matter to count outcomes of events. It also defines permutation as arrangements of objects where order matters and combination as selections of objects where order does not matter. Formulas are given for counting permutations and combinations of distinct objects. Examples demonstrate calculating the number of ways to arrange or select objects in different scenarios.
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The document discusses permutations and combinations. It begins by introducing permutations as arrangements of objects in a definite order. It then presents the fundamental principle of counting, which states that if one event can occur in m ways and is followed by another that can occur in n ways, the total number of occurrences is m×n. It provides examples of using this principle to count outcomes. The document then defines permutations more specifically as arrangements of a number of objects taken some or all at a time. It presents a theorem stating the formula to calculate the number of permutations of n distinct objects taken r at a time is nPr = n(n-1)(n-2)...(n-r+1).
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The document discusses permutations and combinations. It explains that permutations calculate arrangements where order matters, while combinations calculate arrangements where order does not matter. The fundamental counting principle is introduced as a way to calculate the total number of possible outcomes by multiplying the number of options for each part. An example shows there are 120 ways for 5 students to arrange themselves in 5 consecutive seats, using the fundamental counting principle.
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- Examples demonstrate calculating combinations in situations like selecting committee members or players for a team when certain items must or cannot be included.
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This document discusses counting techniques including permutations and combinations. It provides examples of using the fundamental counting principle to calculate the number of possible outcomes in situations like selecting shirts from various sizes and colors or generating license plates from letters and numbers. The key concepts of permutations, which involve ordered arrangements, and combinations, which involve unordered selections, are explained along with related formulas. Practice problems apply these techniques to scenarios such as seating arrangements, word rearrangements, and group selections.
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The document discusses permutations and combinations in the context of seating arrangements. It provides examples to determine the number of possible arrangements for seating groups of people. For a group of 3 people, there are 6 possible arrangements. For a group of 5 people, there are 120 possible arrangements, found by multiplying 5 x 4 x 3 x 2 x 1. The document also discusses using permutations and combinations to solve other types of problems involving arrangements and selections where order does or does not matter.
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1. The document contains examples and formulas for permutations and combinations. It discusses linear permutations, distinguishable permutations, circular permutations, and ring permutations.
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This document discusses permutations and combinations. It defines permutations as arrangements that consider order, and combinations as arrangements where order does not matter. The document provides examples of using formulas and the fundamental counting principle to calculate the number of permutations and combinations in different scenarios, such as selecting committees from a group of people or hands of cards from a deck. It emphasizes that there are always fewer combinations than permutations since combinations ignore order.
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The document discusses permutations and combinations. It defines a permutation as an arrangement of objects where order matters, and a combination as an arrangement where order does not matter. It provides examples of permutations of sets with 3 and 8 elements. The number of permutations of a set of n elements is n factorial. Permutations are arrangements of all elements of a set. The document also provides examples of calculating the number of permutations in different scenarios like seating arrangements and rearrangements of letters in a word.
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This document discusses permutation and combination. It defines a permutation as an arrangement of objects in a definite order, while a combination is a selection of objects where order does not matter. There are two types of permutations - with and without repetition. The number of permutations of n objects taken r at a time without repetition is nPr = n!/(n-r)!, and with repetition is nr. Combinations can be calculated as nCr = n!/r!(n-r)!. Examples of calculating permutations and combinations in different scenarios are provided.
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This document defines and provides examples of permutations and combinations. Permutations refer to arrangements of objects where order matters, while combinations refer to collections of objects where order does not matter. The key formulas discussed are permutations of n objects taken r at a time (nPr) and combinations of n objects taken r at a time (nCr). Several word problems demonstrate calculating permutations and combinations in different contexts such as arranging letters, selecting teams or committees, and more.
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The document discusses various concepts related to permutations and combinations including:
1) It provides examples to explain the difference between permutations and combinations.
2) It lists the formula for permutations as Npr = n! / (n-r)! and provides an example calculation.
3) It poses several word problems involving permutations and combinations and shows the calculations to arrive at the answers.
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This document discusses principles of counting including factorial notation, the fundamental counting principle, permutations, and combinations. Factorial notation (n!) represents the product of all positive integers less than or equal to n. The fundamental counting principle states that if an activity can be completed in n1 ways and another in n2 ways, they can be completed together in n1*n2 ways. Permutations refer to arrangements of objects that consider order, while combinations only consider groupings without order. Formulas to calculate permutations and combinations are provided along with examples of problems applying these principles.
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permutation & combination
shortcut method of permutation and combination. calculate without formula. The study of permutations and combinations is concerned with determining the number of different ways of arranging and selecting objects out of a given number of objects without actually listing them. There are some basic counting techniques which will be useful in determining the number of different ways of arranging or selecting objects. The two basic counting principle are given below:
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Permutation and combination
- Permutation refers to arrangements that consider order, while combination refers to selections where order does not matter.
- The number of permutations of n distinct objects taken r at a time is nPr = n!/(n-r)!, while the number of combinations is nCr = n!/r!(n-r)!.
- Examples are given to illustrate permutations involving restricted arrangements and circular permutations. Restricted permutations consider cases where certain objects are always or never included.
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Applied Math 40S February 28, 2008
There are 5 people that can be seated in a straight line. This can be calculated using permutations, which is 5P1 = 5 ways.
Six students can be seated in 8 vacant seats in 8P6 = 20160 ways.
The document provides examples of calculating permutations and factorials to determine the number of possible arrangements or combinations of objects.
18_permutations_combinations_1.ppt
This document discusses permutations and combinations, which are methods used to solve word problems involving arrangements and selections. It provides examples of permutation problems involving arranging books on a shelf and combination problems involving selecting committee members. The key aspects covered are:
- Permutations consider the order of items, while combinations do not
- Factorials are used to calculate the number of arrangements or selections
- Problems can involve either permutations or combinations, depending on whether order matters
PERMUTATION-COMBINATION.pdf
This document discusses permutations and combinations. It provides formulas for calculating the number of permutations and combinations of n objects taken r at a time. Examples are given to demonstrate calculating permutations and combinations to solve problems involving arranging objects in different orders or selecting objects without regard to order. Practice problems are included for students to calculate unknown values and solve word problems involving permutations and combinations.
Gambling, Probability, and Risk
1. The document discusses probability and counting methods for computing probabilities of events related to gambling and drawing cards from a deck. It introduces concepts like theoretical probability, empirical probability, permutations, combinations, and using factorials and probabilities to solve counting problems.
2. As an example, it calculates the probability of drawing a pair of the same color cards from a deck and determines it is 49% based on counting the possible combinations.
3. It also discusses using probabilities to determine rational betting strategies, like folding unless holding a pair of the same color or suit when playing against others who each drew 2 cards.
PERMUTATION AND COMBINATION.pptx
The document discusses permutation and combination. It provides examples of calculating the number of permutations and combinations in different scenarios like arranging letters to form words or selecting members for a committee. It also solves problems involving permutations and combinations, like calculating the number of 5-digit numbers that can be formed from given digits that are divisible by 4, with and without repetition. The key concepts covered are the formulas for permutation (nPr) and combination (nCr), and knowing when to apply multiplication or addition based on the nature of the problem.
Mat cat que
The document contains 35 math and word problems. The assistant provides concise 3-sentence summaries for each problem:
1) A man discusses promoting entrepreneurship and free education for all. He needs support from others to achieve these goals.
2) The problem asks to rearrange the letters in "PROBLEM" to make 7-letter words without repetition, with the answer being 5040 possible arrangements.
3) The problem asks the probability that the third coin tossed will be heads if 10 coins are tossed simultaneously, with the answer being 1/2 or 512 possible outcomes out of 1024 total.
4) The problem asks to count the ways to post 5 letters into 3 post boxes with any number allowed
Cat,mat,gmat, questions
The document contains questions related to CAT, MAT, GMAT entrance exams. It discusses various topics like probability, permutations and combinations, averages, ratios etc. and provides solutions to sample questions in 3-4 sentences each. The overall document aims to help exam preparation by providing practice questions on common quantitative topics.
Permutation
This document discusses fundamental principles of counting and permutation and combination. It provides examples to illustrate key concepts such as:
1) Mohan has 3 pants and 2 shirts - there are 3×2 = 6 ways to choose a pant and shirt combination.
2) Sabnam has 2 bags, 3 boxes, and 2 bottles - the number of ways to choose one of each is the number of ways to successively choose a bag, box, and bottle.
3) With 4 roads between a student's house and college, there are 4×3 = 12 ways for the student to go to college and return on different roads.
Permutations and Combinations.pptx
The document discusses permutations and combinations of objects. It provides examples of calculating the number of arrangements and selections of objects in different scenarios. For permutations of distinct objects, it gives the formula nPr = n!/(n-r)!. For combinations of objects, it gives the formula nCr = n!/(n-r)!r!. It then works through multiple examples of using these formulas to calculate permutations and combinations in situations like arranging letters, selecting committee members, and choosing balls from boxes.
Week 5 Lecture Math 221 Mar 2012
This document provides information and examples about key probability and statistics concepts for an upcoming quiz. It defines factorial notation, combinations and permutations, and provides examples of calculating them in Minitab. It also defines probability, probability distributions, discrete and continuous distributions, and the binomial and Poisson distributions. Examples are given for each concept to illustrate how to set them up and calculate related values like means, variances, and probabilities.
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Advanced business mathematics and statistics for entrepreneurs
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2. The Western Uplands include Scandinavia, Scotland, and parts of Spain and Portugal. Fjords are characteristic of this glacially-carved region.
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Permutation and combination
- 1. Permutation and Combination for everybody
- 2. In the waiting room of a doctor’s chamber there are three chairs. Five patients, A,B,C,D and E have to be seated on these chairs. In how many ways can we fill up three seats ?