# Arrangements of Boys and Girls

• Sep 24th 2010, 10:26 PM
Lukybear
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?
• Sep 25th 2010, 03:48 AM
Plato
Quote:

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?
• Sep 25th 2010, 06:22 PM
Lukybear
Understood thanks.