prob.part42.87_88 - 3.1. PERMUTATIONS 79 Number of people...

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Unformatted text preview: 3.1. PERMUTATIONS 79 Number of people Probability that all birthdays are different 10 .8830518 20 .5885616 30 .2936838 40 .1087682 50 .0296264 60 .0058773 70 .0008404 80 .0000857 90 .0000062 100 .0000003 Table 3.2: Birthday problem. We now turn to the topic of permutations. Permutations Definition 3.1 Let A be any finite set. A permutation of A is a one-to-one mapping of A onto itself. To specify a particular permutation we list the elements of A and, under them, show where each element is sent by the one-to-one mapping. For example, if A = { a, b, c } a possible permutation σ would be σ = a b c b c a . By the permutation σ , a is sent to b , b is sent to c , and c is sent to a . The condition that the mapping be one-to-one means that no two elements of A are sent, by the mapping, into the same element of A . We can put the elements of our set in some order and rename them 1, 2, .. . , n ....
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This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.

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prob.part42.87_88 - 3.1. PERMUTATIONS 79 Number of people...

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