Strategy:  First find the number of groups of 5 students without regard to
whether the group contains at least 2 boys or not. Then we will calculate
the number of groups to eliminate which contain either no boys (all girls) 
or only one boy (4 girls and 1 boy).

1.  The number of groups of 5 without regard to whether there are at least 2
boys.  That's C(24,5) = 42504.

2.  The number of groups with no boys, (all girls) is C(18,5) = 8568, which
    we must subtract.
3.  The number of groups with only 1 boy and 4 girls. 
    Choose the boy 6 ways.
    For each of those ways, we can choose the 4 girls C18,4) ways.
    That's 6*C(18,4) = 6*3060 = 18360, which we must subtract. 

So we subtract those:

Answer: 42504-8568-18360 = 15576.

Edwin