# 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.

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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`

**Sources:**

Let G stand for girl and B stand for boy

Thus we have two cases

**(i) countng starts from left**

GBGBGBGBGBGBGB

In this arrangment girls can be arrange in 7! and boys can be arranged 7!

Thus by fundamental principle total no. of arrangements are

`7! xx 7! = (7!)^2`

``** (ii) counting starts from right**

BGBGBGBGBGBGBG

In this arrangment girls can be arrange in 7! and boys can be arranged 7!

Thus by fundamental principle total no. of arrangements are

`7! xx7! =(7!)^2`

**Thus total number of possible arrangements are**

`(7!)^2+(7!)^2=2xx(7!)^2`