Permutations & Combinations

Permutations & Combinations - Probability and ways...

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1 Probability and ways of counting (Understanding Powerball) 1) Arrangements of items (also called permutations ) Examples: 1 2 2 1 2 1 2 3 1 3 2 2 1 3 3 1 2 2 3 1 3 2 1 6 1 2 3 4 ?
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2 Develop a procedure Position 1 2 3 4 1 2 3 4 1) 4 choices for placing in position 1 2) then 3 choices for position 2 for each in 1) 3) then 2 choices for position 3 for each in 2) 4) and 1 choice for position 4 for each in 3)
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3 A Diagram (helps understanding) 1 2 3 4 Position
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4 Develop a general rule 2 items: 2 * 1 = 2 3 items: 3 * 2 * 1 = 6 4 items: 4 * 3 * 2 * 1 = 24 r items: r * (r-1) * (r-2) . . . 2 * 1 = r ! The number of arrangements or permutations of r items is given by r ! (“r factorial”) These numbers get big! for r = 10 r ! = 3,628,800 for r = 20 r ! = 2.43x10 18 Most calculators can compute factorials.
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5 2) Arrangements of selected items (still called permutations ) Example: Position 1 2 1 2 3 4 1) 4 choices for position 1 2) 3 choices for position 2 for each in 1)
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6 Diagram 1 2 Position Generalize:
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Permutations & Combinations - Probability and ways...

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