Permutation – Order matters (a race)

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Presentation transcript:

Permutation – Order matters (a race) L6-7 Obj: Students will be able to calculate permutations and combinations Permutation – Order matters (a race) Combination – Order doesn’t matter Factorial ! 8! Means 8*7*6*5*4*3*2*1 = 40320 5! Means 5*4*3*2*1 = 120 2! Means 2*1 = 2 0! = 1

A permutation is an arrangement of items in a particular order A permutation is an arrangement of items in a particular order. Ex 1: In how many different orders can ten dogs line up to be groomed? Ex 2: In how many different orders can the Giants manager arrange the batting lineup? Ex 3: In how many different ways can 6 students line up to buy lunch?

10P4

1. If 7 “friends” are at the park and all start a running race at the same time. If the slowest three get “chosen” in a 1st, 2nd and 3rd slowest order, how many arrangements of these 3 are there? 2. Eight yachts enter a race. How many arrangements of first, second, and third places are possible?

Ex 1: 10 kids try out for 9 positions on a baseball team Ex 1: 10 kids try out for 9 positions on a baseball team. How many different teams can be configured?

Permutations and Combinations 1. 10C4. 5. 10P3 12C3 6. 8P4 10C5 7. 11P5 8C2 8. 7P2

Permutations and Combinations LESSON 6-7 Additional Examples A pizza menu allows you to select 4 toppings at no extra charge from a list of 9 possible toppings. In how many ways can you select 4 or fewer toppings?

Ex. Ten candidates are running for three seats in the student government. Manuel, Riley, and Maddy are three of the candidates. What is the probability that Manuel, Riley, and Maddy all win? Ex 4: A DJ wants to select 5 songs from a new CD that contains 12 songs. How many 5 selections are possible?

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Practice Homework L6-7 (p 354) #2-30e 38 44-62e 73 76 86 88 Expand 2. (y – 2)5 3. (m + 2)7 4. (2x – 1)4 5. (3y – 2)8 Homework L6-7 (p 354) #2-30e 38 44-62e 73 76 86 88