permutation and Combination fall 2011

permutation and Combination fall 2011 - DSCI 2710 SC...

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1 DSCI 2710 Permutation and Combination How Many 4-digit PIN Numbers are Possible? We need to know what are the possible values for each digit. We need to know if a number can be repeated.
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2 Assume Repetition Is Allowed Assume that each PIN digit can be chosen from 0 to 9. If repetition is allowed , then the number of codes is 10 * 10 * 10 * 10 = 10 4 = 10,000 Assume No Repetition Is Allowed Si di it t b Since a digit cannot be repeated, the number of choices decreases each time. The number of possible codes i s 10 * 9 * 8 * 7 = 5040.
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3 Permutations Permutations are how many ways a given number of things can be sequenced. The standard notation is that n P n is the permutations (sequences) of all n things in a set of n things; n P r is the permutations on n things taken r at a time. The relevant formulas are below: n P n = n! n P r = n!/(n - r)! Permutation Example •The number of permutations of 4 things taken 3 at a time is 4!/(4-3)! = 24/1 = 24. •Thus for items, A, B, C, and D, the 24
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This note was uploaded on 01/13/2012 for the course DCSI 3710 taught by Professor Pavur during the Fall '11 term at North Texas.

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permutation and Combination fall 2011 - DSCI 2710 SC...

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