A class of 14 students is made up of 6 girls and 8 boys
Determine the number of different groups of 5 that can be formed
if there must be at most 1 boy in each group (there could be
0 or 1 boy in each group). 

A. 23
B. 30
C. 120
D. 126

If there are no boys, then we only need to eliminate one of the 6 girls.
We can choose the girl to eliminate any of 6 ways

If there is 1 boy, then we may choose the boy any of 8 ways.  For each of
these 8 ways to choose the boy we can choose 4 girls to go with him C(6,4)
ways or 6!/(4!2!) = 720/(24·2) = 15. So that 8·15 
or 120 ways.

The grand total is 6+120 or 126, choice D

Edwin
AnlytcPhil@aol.com