+1443 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?
+399 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?
