In how many ways can 7 boys and 7 girl be lined up if a girl

In how many ways can 7 boys and 7 girl be lined up if a girl must be first in line and girls and boys alternate positions in line.

Solution

Lets take girls as G and boys as B

G,B,G,B,G.......G,B.

The above is how the arrangement will appear to be.

The number of ways in which the girls can be arranged `= 7!`

For each such arrangement the ways in which the boys can be arranged `=7!`

Therefore the total number of arrangements `=(7!)^2`