kapslock wrote:

I am getting an answer of 5!x4x3 = 1440.

_ B _ B _ B _ B _

4 Boys can be rearranged in their prescribed positions in 4! ways.

3 Girls can be placed in 5 spaces in 5x4x3 ways.

Therefore, total = 4! x 5 x 4 x 3 = 5! x 4 x 3 = 1440.

Tyr, could you explain your working in detail please?

You have two times more outcomes then I do.

I think I see where's my flaw.

Classic

Counting number of outcomes where two girls sit together I counted arrangements of three girls together twice.

Number of outcomes where three girls sit together as noted originally - 5! * 3! = 6!

So number of outcomes where two girls sit together is in fact -

6! * 3! - 6!

And outcomes that we want 7! - 6! * 3! + 6! = 2 * 6!

Note to self, remember rules of Venn diagrams