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.
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