One Stop GATE Forum: gate 2006 question no 24

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   please solve this with explanation.the answer given is D

given a set of elements N={1,2,...,n} and two arbitary subsets A and B
of the set N.how many of the n! permutations M from N to N satisfy
min(M(A))=min(M(B)) where min(S) is the smallest integer in the set of
integers S,and M(S) is the set of integers obtained by applying
permutation M to each of the element of S?

A) (n-|A U B|)|A||B|

B) (|A|^2 + |B|^2)n^2

C) n!(|A intersection B|)/(|A U B|)

D) |A intersection B|^2*permutation(n,|A U B|)

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Vijay007 Newbie Joined: 02Feb2007 Online Status: Offline Posts: 19	Topic: gate 2006 question no 24 Posted: 02Feb2007 at 5:17pm
	please solve this with explanation.the answer given is D given a set of elements N={1,2,...,n} and two arbitary subsets A and B of the set N.how many of the n! permutations M from N to N satisfy min(M(A))=min(M(B)) where min(S) is the smallest integer in the set of integers S,and M(S) is the set of integers obtained by applying permutation M to each of the element of S? A) (n-\|A U B\|)\|A\|\|B\| B) (\|A\|^2 + \|B\|^2)n^2 C) n!(\|A intersection B\|)/(\|A U B\|) D) \|A intersection B\|^2permutation(n,\|A U B\|) Post Resume:* Click here to Upload your Resume & Apply for Jobs

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