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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
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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

 

 

cool cool cool

CPhill  Apr 23, 2017

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