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?

Guest Nov 21, 2019

#1**0 **

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

CPhill Nov 21, 2019