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Question

A bag contains n white and n black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is 14,400. then n =


A
6
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B
5
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C
4
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D
3
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Solution

The correct option is B 5
According to the given condition:

$$(^nC_1\ ^nC_1)$$$$(^{n-1}C_1\ ^{n-1}C_1)..........$$$$(^1C_1\ ^1C_1)=14400$$

$$\Rightarrow (^nC^{n-1}C_1.......\ ^1C_1)^2=(120)^2$$

$$\Rightarrow n(n-1)(n-2)....\ 1=120$$

$$\Rightarrow n!=5!$$

$$\Rightarrow n=5$$

Mathematics

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