SOLUTION: There are 2 boys and 5 girls at a party. In how many ways can they sit at a round table, if the boys must not sit next to each other?

Let boy #1 sit down first. Since the table is round we consider it the
same arrangement no matter where he sits.

Let boy #2 sit down next.  Of the 6 remaining chairs, there are only 4
chairs that boy #2 can sit in that are not next to boy #1.

That's 4 ways we can seat the boys.

The 5 girls can then be seated in the 5 remaining chairs
in 5! ways.

Answer 4·5! = 4·120 = 480 ways.

Edwin