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There are n white and n black balls mark...

There are n white and n black balls marked 1, 2, 3, …… n. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours are:-

A

n!

B

(2n)!

C

`2(n!)^2 `

D

`((2n)!)/((n!)^2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Case I: `W_1/1 B_1/2 W_2/3 B_2/4 W_3/5 B_3/6` ......`W_n B_n/(2n^(th)"place")` = n! x n!
Case II:
`B_1/1 W_1/2 B_2/3 W_2/4 B_3/5W_3/6` .....`B_n` `W_n/(2n^(th)"place")` =n! x n!
So number of ways =`2(n!)^2`
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