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Pre-Cal 40S May 6, 2009

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Permutations of Non-Distinguishable Objects and Circular Permutations.

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Pre-Cal 40S May 6, 2009

1. 1. Permutations of Non- Distinguishable Objects and Circular Permutations Poker fun with your best friends by ﬂickr user coltfan909
2. 2. How many four-digit even numbers are there if the same digit cannot be used twice?
3. 3. How many four-digit even numbers are there if the same digit can be repeated?
4. 4. In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?
5. 5. How many different 4 letter quot;wordsquot; can you make from the letters in the word BOOK?
6. 6. K O OB B O OK BOOK KOOB BO K O K O BO BO K O K O BO
7. 7. Permutations of Non- Distinguishable Objects The number of ways to arrange n objects that contain sets of non-distinguishable objects is given by:
8. 8. Example: How many different quot;wordsquot; can be made form the letters in the word: (a) BOOK (b) MISSISSIPPI # of O's = 2 ∴ # of I's = 4 # 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?
10. 10. How many distinguishable ways can 3 people be seated around a circular table?
11. 11. How many distinguishable ways can 4 people be seated around a circular table?
12. 12. Circular Permutations The number of ordered arrangements that can be made of n objects in a circle is given by: (n - 1)! Example: How many different ways can 6 people be seated around a circular table? (6 - 1)! = 5! = 120
13. 13. How many distinguishable ways can 3 beads be arranged on a circular bracelet?
14. 14. Circular Permutations Special Case: A bracelet is a circle that can be ﬂipped over. The number of different arrangements that can be made of objects on a bracelet is: Example: How many bracelets can can be made from 6 different beads? (6 - 1)! = 5! 2 2 = 60
15. 15. How many distinguishable ways can 4 beads be arranged on a circular bracelet?