Probability Day CIRCULAR PERMUTATIONS
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1 Probability Day CIRCULAR PERMUTATIONS Ex. 1 How many ways are there to arrange 4 people around a table? (see SmartBoard link) Ex. 2 How many circular permutations are there of: a. V W X Y Z b. M O N K E Y S Let s make it a little harder: Ex. 3 5 high school kids and 5 junior high kids sit around a circular table for a mentoring program. They must sit every other (jh, hs, jh, hs.) How many ways can they be arranged? Ex. 4 How many different ways can 6 girl scouts hold hands around a circle considering only who is between them, not what side she is on?
2 Gotta think! Determine the following: 1. How many ways are there to line up 7 kids if Brandon must be the first one? 2. How many ways are there to line up 4 freshman and 4 seniors if they must alternate? 3. How many ways are there to line up 8 kids if Chris and Krise insist on being next to each other? 4. How many ways are there to arrange 10 kids around a circular table? 5. 8 children play with play-doh around a circular table at day care. Johnny, Joey, and Jenny are neighbors and insist on sitting next to one another. How many ways are there to arrange these kids around the table? 6. How many ways can you arrange the 12 charms around your bracelet, given that no two charms are the same, considering only which charm is between which, not what side it is on. (I know this is tricky to read, but consider flipping the bracelet upside down the charms are still in between the same charms ) 7. How many ways are there to arrange 3 girls and 3 boys around a circular table if they must alternate?
3 1-3) Focus on the difference between AND and OR 11.4 Practice and Review 1. Matching Marty has 18 pairs of socks, 10 shirts, and 7 pairs of pants. How many different ways can he choose: a. A pair of pants and a pair of socks? b. A pair of pants or a pair of socks. c. A pair of sock, pants, and a shirt. d. A pair of socks, pants, or a shirt. 2. Using the letters I LOVE MATH a. How many ways can you pick a vowel or a consonant? b. How many ways can you pick a vowel and a consonant? c. How many ways can I make a 4 letter word with repetition? d. How many ways can I make a 4 letter word without repetition? e. How many ways can I make a 4 letter word ending in a vowel with M in the second position? 3. There are 22 students in our Trig Honors class, 10 of which are in AP Euro and 15 are in Honors English and 8 students are in both. How many students are in AP Euro OR Honors English. 4. Given a deck of cards, find the number of ways you can choose a 4 or a Spade. 5. How many ways are there to line up 6 kids for a picture? 6. How many ways are there to line up 6 kids if Becky must be the first one? 7. How many ways are there to line up 3 boys and 3 girls if they must alternate? 8. How many permutations of each word are there of the word: MASSACHUSETTS 9. How many ways are there to line up 6 kids if Robbie and Jenni insist on being next to each other? 10. How many ways are there to arrange 6 kids around a circular table?
4 11. You are hosting a dinner party before Turnabout with 8 of your friends. Will insisted upon sitting next to his new girlfriend, Susie. How many different ways can you all sit around a circular table? 11. How many ways can you arrange the 15 charms around your bracelet, given that no two charms are the same, considering only which charm is between which, not what side it is on. 12. How many ways are there to arrange 3 girls and 3 boys around a circular table if they must alternate? 13. For your history class you must do a report on three different states. How many choices of 3 states do you have? 14. How many 5 card hands can you be dealt that are all diamonds? 15. How many 5 card hands can you be dealt that have 3 diamonds and 2 spades? 16. How many 5 card hands can you be dealt that have exactly 2 queens? 17. How many 5 card hands are possible that have all 4 aces? 18. Simplify each expression: a. P b. x 2 2P 0 c. xc x 2 d. 2C 2 e. 5C2 5 C? (something other than 2!)
5 19. A committee of 6 people is being made out of 10 men and 8 women. a) How many committees are there with an equal number of men and women? b) How many committees can be made that are all men? All women? c) How many committees have at least 1 woman? d) How many committees can be made if Gerta must be on it? 20. Out of 12 people, how many committees can be made with either 4 or 5 members?
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