There are six boys and girls who sits in one row. Find the probability that no two boy sits together.
If there are six boys and six girls, then we can arrange them in a row in 12! ways.
If no two boys sit together, then either:
- the boys sit in places 1, 3, ..., 11 (and the girls in places 2, 4, ..., 12); or
- the boys sit in places 2, 4, ..., 12 (and the girls in places 1, 3, ..., 11)
Each of these arrangements can be done in 6! x 6! different ways. So the probability that one of these occurs is