# Let A be a set containing n elements. A subset P of the set A is chosen at random. The set A is reconstructed by replacing the elements of P, and another subset Q of A is chosen at random. The probability that PnQ contains exactly m (m

Question : Let A be a set containing n elements. A subset P of the set A is chosen at random. The set A is reconstructed by replacing the elements of P, and another subset Q of A is chosen at random. The probability that PnQ contains exactly m (m<n) elements is

(A) $\dfrac{3^{n-m}}{4^{n}}$

(B) $n_{C_{m}}\times \dfrac{3^{m}}{4^{n}}$

(C) $n_{C_{m}}\times \dfrac{3^{n-m}}{4^{n}}$

(D) none of these

Answer : option (C)

Solution :

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