There are 5 boys and 4 girls in my class. All of them are distinguishable.
In how many ways can they be seated in a row of 9 chairs such that at least 3 girls are all next to each other?
+130517 3 girls can sit together in groups of 3 in chairs 1 - 7.....and they can be arranged in 3! ways for each of these seatings
And for each of these seatings, the boys can be seated in 5! ways
And 4 girls can sit together in groups of 4 in chairs 1 - 6.....and they can be arranged in 4! ways for each of these seatings
And for each of these seatings, the boys can be seated in 5! ways
So...the total arrangements =
7 * 3! * 5! + 6 * 4! * 5! = 22,320 arrangements
