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January 17th, 2011, 07:37 AM   #1
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permutation problem

A non-empty P is formed by selecting elements randomly WOR from a set B consisting of n (>1) distinct elements. Another non-empty subset Q is formed in similar fashion from the original set B consisting of those same n elements. Then what is the probability that P and Q do not have any element common between them?
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January 17th, 2011, 01:08 PM   #2
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Re: permutation problem

Assume P has k elements and Q has j elements, the probability of nothing in common is:
(n-j)!(n-k)!/[n!(n-j-k)!]
Note that j+k?n, otherwise the denominator is ? and the probability = 0.

Exercise for the reader - derive this expression!
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