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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?

 

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

 Mar 13, 2024
 #1
avatar+394 
+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?

 Mar 14, 2024

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