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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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Permutations combinations
Permutations / Combinations

I. Permutations

A) Factorials

B) Permutations nPr n!

(n-r)!

II. Combinations nCr n!

r! (n-r)!


Factorials
Factorials !

  • 5!

    5x4x3x2x1 = 120

  • How many ways can 10 people line up in a straight line?

    10! = 3,628,800


Permutations
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


Combinations
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


Permutations combinations in your calculator
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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