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):
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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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