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a) A baking club wants to form an executive committee. There are 12 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 4 people?

b) A baking club wants to form an executive committee. There are 12 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 4 people, including Mark?

c) A baking club wants to form an executive committee. There are 12 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 4 people, not including Mark?

Sep 23, 2023

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a)

There are 12 people and we want to pick 4 of them. So, we use

\(\binom{12}{4} = 495\)

b)

First, we know that Mark has to be on the committee, so we put him in immediately. This leaves 3 spots to be filled by 11 people. Hence we use

\(\binom{11}{3} = 165\)

c)

We know that mark cannot be included, so there are 11 people who can go in 4 spots.

\(\binom{11}{4} = 330\)

I hope these are correct!

Sep 27, 2023