Question

There are $n$ distinct white and $n$ distinct black balls. If the number of ways of arranging them in a row so that neighboring balls are of different colors is $1152$ then find the value of ${}^{\prime }{n}^{\prime }$.

Answer 1

Number of arrangements are $2n!n!$

Given that $2n!n!=1152$

$\Rightarrow (n!{)}^2=576$

$\Rightarrow n!=24$

$\Rightarrow n=4$.