6.7 Permutations & Combinations. Permutations / Combinations I.Permutations A) Factorials B) Permutations n P r n! (n-r)! II. Combinations n C r n! r!

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Presentation transcript:

6.7 Permutations & Combinations

Permutations / Combinations I.Permutations A) Factorials B) Permutations n P r n! (n-r)! II. Combinations n C r n! r! (n-r)!

Factorials ! 5! 5x4x3x2x1 = 120 How many ways can 10 people line up in a straight line? 10! = 3,628,800

Permutations n P r = n! n = total # of items (n-r)! r = items in a set arranged r items at a time How many 4 – letter codes can be made if no letter can be used twice? First, identify the “n”:26 because there are 26 letters in the alphabet Second, identify the “r”: 4 because it says how many 4… 26!26x25x24x23x22x21x20…. (26-4)! 22x21x20… 26x25x24x23 =358,800

Combinations I have 6 scarfs, each a different color. I want to wear 2 at a time. How many combinations are there? Think: Purple, Orange, Blue, Green, Yellow, Red Combinations: PO, PB, PG,PY, PR, OP?? C 2 6!6x5x4x3x2x1 2! (6-2)!(2x1) (4x3x2x1) 6x5 = 30 2x1 = 2 Final Answer: 15

Permutations/Combinations in Your Calculator 26 P 4 Put Into Your Calculator: 358,800 5! Put Into Your Calculator: C 2 Put Into Your Calculator: 15