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

Options

A. `n!`
B. `(2n)!`
C. `2(n!)^(2)`
D. `((2n)!)/((n!)^(2))`

Answer

C

Explanation

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!xx!`
CaseII
`(B_(1))/1 (W_(1))/2(B_(2))/3(W_(2))/4(B_(3))/5 (W_(3))/6……….B_(n)(W_(n))/(2n^(th)"place")=n!xxn!`
Son number of ways `=2(n!)^(2)`