+190 A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?
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A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?
Excluding Mark, there are 14 members left to choose from.
There are 14 choices for the first member of the committee.
After the first is chosen, 13 choices are left for the second.
14 x 13 = 182 ways to form the committee.
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The above possiblity presupposes the two members have different titles, such as president and vice president.
In such case, for example, Janet & Frank would be different from Frank & Janet. If there are no differentiations
between the two members, however, the possibilities would be halved, and the total number would be 91 ways.
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