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 14400 , then $n$ is equal to

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Aicharya · Accepted Answer

According to the given condition $\left({ }^n C_1{ }^n C_1ight)\left({ }^{n-1} C_1{ }^{n-1} C_1ight) \ldots\left({ }^1 C_1^1 C_1ight)=14400$ $\begin{aligned} & \Rightarrow \quad\left({ }^n C^{n-1} C_1 \ldots{ }^1 C_1ight)^2=(120)^2 \ & \Rightarrow \quad n(n-1)(n-2) \ldots 1=120 \ & \Rightarrow \quad n !=5 	ext { ! } \ & \Rightarrow \quad n=5 \ & \end{aligned}$

A bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement…

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