In how many ways 3 girls and 3 boys be seated in a row of 6 chairs if 1 boy and 1 girl refused to sit next to each other?
First we find the number of permutations of the 3 girls and 3 boys filling the 6 chairs, this is not accounting for the two who won't sit together.
For the number of ways with the two who refuse to sit together being put together:
If the said boy is in seat 1 and girl in seat 2.
If the said boy is in seat 2 and girl in seat 1.
If we do this for seat 2 & 3, 3 & 4 etc. We find we have:
We therefore need to subtract this from