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, including Mark?

Answer 1

To determine how many ways the baking club can form an executive committee with 2 people, including Mark, we start by recognizing that the committee must include Mark and one additional member chosen from the remaining members of the club.

There are 15 people in the baking club, and Mark is one of them. This leaves 14 other members to choose from.

Since the committee must include Mark, the second member of the committee can be any one of the remaining 14 members. Therefore, the number of ways to choose this second member is given by:

\[
\binom{14}{1}
\]

The binomial coefficient \(\binom{14}{1}\) calculates the number of ways to choose 1 member out of 14, which is simply:

\[
\binom{14}{1} = 14
\]

Therefore, the number of ways to form an executive committee of 2 people that includes Mark is:

\[
\boxed{14}
\]