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January 17th, 2011, 07:37 AM  #1 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  permutation problem
A nonempty P is formed by selecting elements randomly WOR from a set B consisting of n (>1) distinct elements. Another nonempty 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?

January 17th, 2011, 01:08 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697  Re: permutation problem
Assume P has k elements and Q has j elements, the probability of nothing in common is: (nj)!(nk)!/[n!(njk)!] Note that j+k?n, otherwise the denominator is ? and the probability = 0. Exercise for the reader  derive this expression! 

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