# Math Help - Arrangements of Boys and Girls

1. ## Arrangements of Boys and Girls

How many ways can 4 different boys and 4 different girls be arranged in a line if
a) girls and boys alternate

My logic is:
arrange boys first, there are 4! ways of arrangement
There are then 5P4 ways of arranging girls, consider one may be before a boy or after a boy

So this is not the right answer. But where is the flaw in my logic. Where did i over count?

2. Originally Posted by Lukybear
How many ways can 4 different boys and 4 different girls be arranged in a line if a) girls and boys alternate.
In your count the girls and boys may not alternate.
Answer: $2\cdot(4!)^2$. WHY?

3. Understood thanks.