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Q.

A bag contains n white and n black balls. Pairs of balls are drawn without replacement until the bag is empty. If the number of ways in which each pair consists of one black and one white ball is 576, then n =

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a

4

b

8

c

16

d

24

answer is A.

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Detailed Solution

The number of way of selection of pairs of balls consists one black ball and one white ball

$\begin{array}{l} = (^{n} C_{1}) (^{n} C_{1}) (^{n - 1} C_{1}) (^{n - 1} C_{1}) \dots \dots . (^{1} C_{1}) (^{1} C_{1}) \\ = {(^{n} {C_{1}}^{n - 1} {C_{1}}^{n - 2} C_{1} \dots . .^{1} C_{1})}^{2} = 576 \\ [n (n - 1) (n - 2) \dots 1] = (24) \Rightarrow n! = 24 = 4! \\ ∴ n = 4 \end{array}$

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