math
posted by bballer .
Suppose that a department contains 11 men and 19 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

cases:
6W0M
5W1M
4W2M
3W3M  no good
number of cases
= C(19,6) x C(11,0) + C(19,5) x C(11,1) + C(19,4) x C(11,2)
= 27132 + 127908 + 213180
= 368220