Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
1374 Upvotes
Verified Answer
The correct answer is:
5
According to the given condition
$\left({ }^n C_1{ }^n C_1\right)\left({ }^{n-1} C_1{ }^{n-1} C_1\right) \ldots\left({ }^1 C_1^1 C_1\right)=14400$
$\begin{aligned} & \Rightarrow \quad\left({ }^n C^{n-1} C_1 \ldots{ }^1 C_1\right)^2=(120)^2 \\ & \Rightarrow \quad n(n-1)(n-2) \ldots 1=120 \\ & \Rightarrow \quad n !=5 \text { ! } \\ & \Rightarrow \quad n=5 \\ & \end{aligned}$
$\left({ }^n C_1{ }^n C_1\right)\left({ }^{n-1} C_1{ }^{n-1} C_1\right) \ldots\left({ }^1 C_1^1 C_1\right)=14400$
$\begin{aligned} & \Rightarrow \quad\left({ }^n C^{n-1} C_1 \ldots{ }^1 C_1\right)^2=(120)^2 \\ & \Rightarrow \quad n(n-1)(n-2) \ldots 1=120 \\ & \Rightarrow \quad n !=5 \text { ! } \\ & \Rightarrow \quad n=5 \\ & \end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.