First slide

Permutations

Question

A group of 2n students consisting of n boys and n girls are to be arranged in a row such that adjacent members are of opposite sex. The number of ways in which this can be done is

Moderate

A

$2 (n!)$
B

$(n!)$
C

$2 {(n!)}^{2}$
D

$n!$

Solution

. There are following ways for the photograph.
$M_{1} W_{1} M_{2} W_{2} \dots M_{n} W_{n}$
or $W_{1} M_{1} W_{2} M_{2} \dots W_{n} M_{n}$
This can be done in $(2) (n!) (n!) = 2 {(n!)}^{2}$ way.

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