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6.7 Permutations & Combinations

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6.7 Permutations & Combinations

I.Permutations

A) Factorials

B) Permutations nPr n!

(n-r)!

II. Combinations nCr n!

r! (n-r)!

- 5!
5x4x3x2x1 = 120

- How many ways can 10 people line up in a straight line?
10! = 3,628,800

- 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

- 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??.....
- 6C26!6x5x4x3x2x1
2! (6-2)!(2x1) (4x3x2x1)

6x5 = 30

2x1 = 2

Final Answer: 15

- 26P4 Put Into Your Calculator: 358,800
- 5! Put Into Your Calculator: 120
- 6C2 Put Into Your Calculator: 15