SOLUTION: 5 girls and 4 boys sit in a row. If only two boys sit next to each other , find the number of permutation.

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Question 1070372: 5 girls and 4 boys sit in a row. If only two boys sit next to each other , find the number of
permutation.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We line up the 5 girls in 5!=120 ways.  

_G_G_G_G_G_

Next we will insert the boys among the girls. There are 6 insertion
places to choose for the boys to be inserted, indicated above by "_"'s.

We choose two boys to sit together left to right in 4*3 = 12 ways.
We choose an insertion place for that pair of boys any of 6 ways.
We choose a different insertion place for the older of the two 
remaining boys any of 5 ways.
We choose another different insertion place for the one remaining boy 
any of 4 ways.

Answer: (120)(12)(6)(5)(4) = 172800 ways.

Edwin