There are 5 boys and 4 girls in my class. 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

Guest Apr 23, 2017

#1**+2 **

Notice that this is equivalent to finding the the total number of possible arrangements less the number of arrangements where none of the boys sit together

Since the total number of students = 9, the total number of arrangements = 9!

And the arrangement that would have none of the boys sitting together would look like this :

B G B G B G B G B

And we have 5! ways to arrange the boys and 4! ways to arrange the girls

So.....the total number of arrangements where none of the boys sit together = 5! * 4!

So....the total ways in which they can be arranged with at least two boys next to each other =

9! - 5! * 4! = 362880 - 360,000 = 2880

CPhill
Apr 23, 2017