Question

In how many ways can three girls and four boys be arranged in a a row of seven seats with the girls in consecutive seats?

Answer 1

Since the girls have to sit together, consider them all as one thing. So instead of 7 people, 3 girls and 4 boys, think of it like 1 girl group and 4 boys taking up a place. Now from there you might realize that this is out of 5 total locations, and really the boys can be placed really everywhere else and it doesn't really matter as far as the girls are concerned. So forget about the guys for second, since they'll just go wherever is leftover.

So you can put the group of girl in 1 of 5 locations right? So there are 5 ways to to place the group of girls on the bench. But now within each group of girls and boys, they can be arranged right? So for each of those 5, we know there are 3! ways to arrange the girls and 4! ways to arrange the boys.

5*3!*4! is how many different ways. You just need to separate the groups apart, that's really all.