Two brothers and three sisters form a single line for a photograph. The two boys refuse to stand next to each other. How many different line-ups are possible?
Let the positions be A B C D E from left to right
There are C(5,2) = 10 possible positions that the boys can occupy
But only 4 of them are together
AB BC CD DE
So....6 of them aren't
And for each of these, the boys can be arranged 2 ways
And for each arrangement of the boys, the girls can be arranged in 3! = 6 ways
So......the number of possible line-ups =
6 * 2 * 6 = 72 possible line-ups