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The committee must consist of a chairman and some number of members-at-large. How many ways can the committee be chosen? There must be least one member-at-large.  (For example, suppose that Alex is chair while Betty, Carl, and D'Angelo make up the committee. This counts as the same as Alex being chair while Carl, Betty, and D'Angelo make up the committee. It is not the same as Betty being the chair, with Alex, Carl, and D'Angelo making up the committee. It is also not the same as Alex being chair with the committee consisting of Betty and Carl.)

 Oct 30, 2020
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There are 414 ways to form the committee.

 Oct 30, 2020

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