6.7 Permutations &amp; Combinations

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# 6.7 Permutations &amp; Combinations - PowerPoint PPT Presentation

6.7 Permutations &amp; 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

Permutations / Combinations

I. Permutations

A) Factorials

B) Permutations nPr n!

(n-r)!

II. Combinations nCr 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
• 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
• 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