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 row so that the adjacent balls are of different colours is ______.

Options

• (2n + 2)!

• (2n + 2)! × 2

• (n + 1)! × 2

• 2((n + 1)!)²

Answer 1

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 row so that the adjacent balls are of different colours is `underlinebb(2((n + 1)!)^2)`.

Explanation:

Ways to arranged white balls = |n + 1 

Ways to arranged black balls so that

No adjacent balls are same colour is `2^(n + 1)C_(n + 1)` |n + 1 = 2|n + 1

Total ways = 2(|n + 1)²