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A baking club wants to form an executive committee.  There are \$18\$ people in the baking club, including Mark.  In how many ways can the baking club form an executive committee with \$2\$ people?

A baking club wants to form an executive committee.  There are \$18\$ people in the baking club, including Mark.  In how many ways can the baking club form an executive committee with \$2\$ people, including Mark?

A baking club wants to form an executive committee.  There are \$18\$ 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?

May 2, 2024

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Here's my take:

A baking club wants to form an executive committee.  There are \$18\$ people in the baking club, including Mark.  In how many ways can the baking club form an executive committee with \$2\$ people?

It's just \(\binom{18}{2}\)because you just have to choose \(2\) people out of the 18 candidates.

\(\binom{18}{2}\)= \(\boxed{153}\).

A baking club wants to form an executive committee.  There are \$18\$ people in the baking club, including Mark.  In how many ways can the baking club form an executive committee with \$2\$ people, including Mark?

Well, one of the spots is taken (by Mark), and there are 17 candidates left, with 1 spot left, so it's just \(\binom{17}{1}\), or \(\boxed{17}\).

A baking club wants to form an executive committee.  There are \$18\$ 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?

For this one, because Mark is no longer a candidate that can be put on the committee, that would leave 17 candidates, and 2 need to be chosen, so it would just be \(\binom{17}{2}\), or \(\boxed{136}\)