Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B the same number of elements, is
Options:
A .  
2nCn22n
B .  
12nCn
C .  
1.3.5....(2n−1)2n
D .  
3n4n
Answer: Option A : A We know that the number of sub-sets of a set containing n elements is 2n. Therefore the number of ways of choosing A and B is 2n.2n=22n We also know that the number of sub-sets (of X) which contain exactly r elements is nCr. Therefore the number of ways of choosing A and B, so that they have the same number elements is (nC0)2+(nC1)2+(nC2)2+....+(nCn)2=2nCn Thus the required probability = 2nCn22n.
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