SOLUTION: 7 boys and 6 girls sit in a row. What is the probability of having a boy at each end

Let these 13 blanks represents the seats:

_ _ _ _ _ _ _ _ _ _ _ _ _


We calculate the number of ways this can happen,
with the other 11 people seated between the boys. 

B _ _ _ _ _ _ _ _ _ _ _ B

and then we'll divide by 13!, the number of ways 
anybody can sit anywhere.

For 

B _ _ _ _ _ _ _ _ _ _ _ B

we choose the boy on the left in 7 ways and the boy on the right
in 6 ways, and the 11 remaining people in the middle in 11! ways.

So that's 7×6×11! successful ways, with boys on each end.

Now we'll divide that by 13!



Edwin