Permutations and Combinations

1. Permutations
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2. What is
Permutation?
PERMUTATION refers to the arrangement of objects
in a set. It is the arrangement of objects in a definite
order.
In short, ORDER MATTERS.

3. Rules of
Permutation
Rule 1: Linear Permutation Rule 2: Permutation of n
objects taken r at a time
Rule 3: Permutation with
Repetition
Rule 4: Permutation of
Things that are Alike
Rule 5: Circular Permutation

4. Linear permutation is an ordered arrangement of objects in a line.
When you arrange objects in a straight line, they start with one
fixed position and end on a fixed position.
n is the total number of objects in a set
“!” - denotes a factorial
To solve n factorial, you need to list down the
total number of objects up until it reaches 1.
7! = 7. 6. 5. 4. 3. 2.1
= 5 040

5. Consider the following examples:
In how many ways can you arranged 6 different potted plants in a row?
6P6 = 6!
= 6.5.4.3.2.1
= 720 ways
In how many ways can 4 volleyball players be seated on a bench?
4P4 =4!
= 4.3.2.1
= 24 ways

6. n is the total number of objects in a set
r is the number of selected objects in a set
Analyze the following examples:
In how many ways can 4 different bicycles be parked if there are 7
available parking spaces?

7. Example 2:
Ten runners join a race. In how many ways can they be arranged as
first, second, and third placers?

8. Consider the following examples:
From the set of first 10 natural numbers, you are asked to make a
four-digit number. How many different permutations are possible if
the digits can be repeated?

9. Example 2: If repetition is not allowed
If repetition is not allowed, subtract the total number of objects by 1.
The number you get after subtraction must be multiplied by your n.

10. If there are non-repeating letters in a word, the formula to be used is
n!. On the other hand, if there are letters that are repeated, these
items must be listed down as the denominator.
Example 1:
In how many ways can the letters of the word MESSAGES be
arranged?

11. Example 1:
= 3,360 ways

12. Example 1:
Find the number of different ways that a family of 6 can be seated
around a circular table with 6 chairs.

13. Example 2:
In how many ways can you arrange 5 different colored beads in a
bracelet?

14. Combinations
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15. What is a
Combination?
COMBINATION is a selection of r objects from n
objects in a set where the order of the objects does
NOT MATTER.

16. Combination without
Repetition
Combination with
Repetition

17. Combination without repetition means you cannot choose the same
object or person twice.
Consider these following examples:
How many combinations are possible for 9 objects taken 4 at a time?

18. = 126 possible combinations

19. Combination with repetition simply means you can choose the same
objects or person twice.
1.) How many different combinations of 5 objects are possible
from 9 objects where repetition is allowed?

20. = 1287 possible
combinations

21. "There should be no
such thing as boring
mathematics."
Edsger Dijkstra
Thank You for Listening! We hope you learned something.