2013 AMC 10A Problems/Problem 11
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Problem
A student council must select a two-person welcoming committee and a three-person planning committee from among its members. There are exactly 10 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?
Solution
Let the number of students on the council be . We know that there are
ways to choose a two person team. This gives that
, which has a positive integer solution of
.
If there are people on the welcoming committee, then there are
ways to choose a three-person committee.
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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All AMC 10 Problems and Solutions |