Question

There are $n$ distinct white and $n$ distinct black balls. The number of ways of arranging them in a row so that neighbouring balls are of different colours is:

• A. $n+1C_2$
• B. $\left(2\right)(n!{)}^2$
• C. $\frac{(n!)}{2}$
• D. $noneofthese$

Answer 1

The correct option is B $\left(2\right)(n!{)}^2$

Possible arrangements are BWBW....... or WBWB......

For combination BWBW..... , n blacks can permutate in n! ways and n white balls can permutate in n! ways

Total number of arrangements are (n!)(n!)

Since there are two possible arrangements total ways =$2{(n!)}^2$