Question

There are (n+1) white and (n+1) black balls each set numbered 1 to (n+1). The number of ways in which the balls can be arranged in a row so they the adjacent balls are of different colours is ?

Answer 1

`2*[(n+1)!]^2`

Explanation:

Visually, there are two situations in which the colours will wind up alternating. These will appear as either:
BWBWBW....
or
WBWBWB....
That's where the factor of 2 comes from.

We multiply 2 by the number of ways of rearranging the n+1 white balls. That is `(n + 1)!`. We also multiply it by the number of ways of rearranging the black balls. Another `(n + 1)!`. The answer is
2`[(n+1)!]^2`.