# 6-4 - 6-4 Permutations and = n ×(n-1 ×(n – 2 ×… ×2...

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Unformatted text preview: 6-4 Permutations and CombinationsFACTORIALn! = n ×(n-1) ×(n – 2) ×… ×2 ×1e.g., 4! = 4 ×3 ×2 ×1Note: 4! = 4 ×3! In general, n! = n ×(n – 1)!Permutation: •a selection of a pre-specified number of items from a given set of items, where•different orderings of the same items are considered to bedifferent selections (and are counted separately)Example: set of items = {red, orange, yellow, green}some permutations, selecting 3 at a time:(red, orange, yellow)(orange, red, yellow)(yellow, green, red)(green, yellow, orange)•are there any more? how many are there in all?•you don’t need to list them all and then count themHere’s a formula (based on the multiplication principle):The number of permutationsof nthings taken rat a time is denoted by nPr, or Pn,rand the formula is:nPr= n ×(n - 1) ×(n-2)…(for rfactors)(formula different from book’s but equivalent and easier to use)To answer the above question:The number of permutations of 4 things taken 3 at a time:4P3= 4×3×2 = 246-4p. 1Combination...
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6-4 - 6-4 Permutations and = n ×(n-1 ×(n – 2 ×… ×2...

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