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6.7 Permutations & Combinations

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?

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6.7 Permutations & Combinations

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  1. 6.7 Permutations & Combinations

  2. Permutations / Combinations I. Permutations A) Factorials B) Permutations nPr n! (n-r)! II. Combinations nCr n! r! (n-r)!

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

  4. Permutations • nPr = 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

  5. 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??..... • 6C2 6! 6x5x4x3x2x1 2! (6-2)! (2x1) (4x3x2x1) 6x5 = 30 2x1 = 2 Final Answer: 15

  6. Permutations/Combinations in Your Calculator • 26P4 Put Into Your Calculator: 358,800 • 5! Put Into Your Calculator: 120 • 6C2 Put Into Your Calculator: 15

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