+1314 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 2 boys are next to each other?
+129852 Here's my best shot......
The number of total arrangements possible = 9!
The number of arrangements where no boys sit together is the one where the boys sit in chairs 1, 3, 5, 7 and 9, and the girls sit in chairs 2,4,6 and 8
And there are 5! ways to arrange the boys in this arrangement and 4! ways to seat the girls.
So ....every other arrangement will have at least two boys sitting together...and the number of these =
Number of total possible arrangements - the number of arrangements where no boys sit together =
9! - 5!*4! = 360,000
