SOLUTION: 6girls and 2 boys are to be seated in a row.Find the number of ways that this can be done if the 2boys must have exactly 4girls seated between them.

Question 1132775: 6girls and 2 boys are to be seated in a row.Find the number of ways that this can be done if the 2boys must have exactly 4girls seated between them.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

There are 8 seats; to have 4 girls between the 2 boys, the boys can be in any of three pairs of seats -- 1st and 6th, 2nd and 7th, or 3rd and 8th. So

(1) 3 ways to choose the two seats for the boys.

In those two seats, the two boys can be in either of two orders:

(2) 2 ways to choose which boy is in which seat.

Then the 6 girls can be seated in the remaining 6 seats in 6! ways.

(3) 6!=720 ways to seat the 6 girls.

Total number of ways: 3*2*720 = 4320
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