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In how many ways can 6 girls and 2 boys sit in a row if the 2 boys insist on sitting next to a girl?

 Dec 1, 2021
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Just say the boys DO sit together

they can be in  pos 1&2 or 2&3 or 3&4 or 4&5 or 5&5 or 6&7 or 7&8    that is 7 ways.  

But either boy can be first so I have to times that by 2.

14 ways for the boys to sit together.   Once they are sitting there are 6! ways to sit the girls 

14*6! = 10080 ways for the boys to sit together.

 

With no restrictions there are  8!  ways to sit the kids,

 

With the restrictions, there are     8! - 16*6!  =  6!(56-16) = 6!*40 =   28 800 ways.

 Dec 1, 2021

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