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?

What do you notice about your answers to all three parts?

blackpanther Mar 13, 2024

#1**+2 **

1)

Choosing any 2 random people is 18 choose 2 = ** 153**.

2)

Choosing Mark and 1 other person is just ** 17**, because there are 17 other people.

3)

Exclude mark essentially, so now we calculate 17 choose 2 = ** 136**.

4)

__136 (our answer to #3) + 17 (our answer to #2) = 153(our answer to #1). Why do you think that might be?__

hairyberry Mar 14, 2024