1. ## combinations

there are 14 teachers in a mathematics department. How many 4 person committees can be formed if Mr. G and Mrs. F, 2 of the
14, must be on the committee?

There are 14 teachers in a mathematics department.
How many 4-person committees can be formed if Mr. G and Mrs. F must be on the committee?
Since Mr. G and Mrs. F are already on the committee,
. . we must choose the other two from the remaining twelve teachers.

There are: . ${12\choose2} \:=\:66$ ways.