Probability
posted by Anna .
A school has 8 math teachers, 6 English teachers, and 2 geography teachers. From this group, a 5 teacher committee is required. Calculate the number of ways that this committee can be formed if at least one geography teachers must be on the committee.

The number of committees without restrictions is C(16,5) = 4368
The number of committees without any geography teachers is C(14,5) = 2002
So the number of ways with at least one geography teacher is 43682002 = 2366
or:
1 geography teacher : C(2,1)*C(14,4) = 2002
2 geography teachers : C(2,2)*C(14,3) = 364
sum = 2002+364 = 2366 (as above)