There are n+1 white and n+1 black balls each set number 1 to n+1. The number of ways in which they can be ?

Question

arranged in a row so that the adjacent balls are of different color

Answer 1

the number of ways of arranging just the white balls: (n+1)!

.. . . the black balls: (n+1)!

also, either the black or the white is the leftmost .. . . this means.. we multiply the result by 2

this means: the balls are either

BWBWBWBW.. or

WBWBWBWB...

thus the answer:

2 [(n+1)!]^2