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# Pre-Cal 40S Slides November 27, 2007

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In today's class we learned about permutations and permutations of non-distinguishable objects.

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Statistics
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### Pre-Cal 40S Slides November 27, 2007

1. 1. Permutations ... continued ... At the end of this class answer the question: Why did we start by looking at this picture? Sonicwall
2. 2. (a) How many numbers of 5 different digits each can be formed from the digits 0, 1, 2, 3, 4, 5, 6? (b) How many of these numbers are even? not zero (c) How many of these numbers are divisable by 5? verify this result
3. 3. How many phone numbers can be made under the following conditions: (First digit cannot be 0 or 1 because you'll get the operator or long distance.) • The first two digits are 3 followed by 6 • The third digit is even • The fourth digit is greater than 5 • The fifth and seventh digits are odd • The sixth digit is 2
4. 4. Permutation: An ordered arrangement of objects without repetition. Formula: A.K.A the quot;Pickquot; formula. n is the number of objects to pick from r is the number of objects to be arranged is read as quot;n pick rquot; means: Given a set of n objects, how many ordered arrangements can be made using only r of them at a time? Example: There are 8 horses in a race. In how many ways can three of them finish first, second and third? Solution by the Fundamental Solution as a Permutation Principle of Counting 8 • 7 • 6 = 336 1st 2nd 3rd
5. 5. How many ways can the batting order of a 9-member softball team be listed?
6. 6. A 120-room hotel has reservations from 6 guests for 6 different rooms. In how many ways can the rooms be assigned?
7. 7. How many different quot;wordsquot; can you make from the letters in the word BOOK?
8. 8. Permutations of Non-Distinguishable Objects The number of ways to arrange n objects that contain sets of non-distinguishable objects is given by: Example: How many different quot;wordsquot; can be made form the letters in the word: (a) BOOK (b) MISSISSIPPI # of I's = 4 # of O's = 2 ∴ # of S's = 4 # of P's = 2 ∴
9. 9. How many different quot;wordsquot; can you make from the letters in the word STATISTICS?