Question
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
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.
Was this answer helpful ?
:
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.
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution