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Q.

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, is

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a

(2n)!(n!)2

b

n !

c

2(n!)2

d

( 2n) !

answer is C.

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Detailed Solution

We can arrange n white and n black balls alternately in the following ways:

(i) W B W B...        (ii) B W B W ...

So, required number of ways =n!×n!+n!×n!=2(n!)2

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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, is