Problem:
A student council must select a two-person welcoming committee and a threeperson planning committee from among its members. There are exactly ways to select a two-person team for the welcoming committee. It is possible for students to serve on both committees. In how many different ways can a three-person planning committee be selected?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of student council members. Because there are ways of choosing the two-person welcoming committee, it follows that , from which . The number of ways to select the three-person planning committee is .
The problems on this page are the property of the MAA's American Mathematics Competitions