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Part A.

Ten people, including Fred, are in the Jazz Club. They decide to form a 3-person steering committee.
How many possible committees can be formed?

Part B.

Ten people, including Fred, are in the Jazz Club. They decide to form a 3-person steering committee.
How many possible committees could be formed that include Fred?

Part C.

Ten people, including Fred, are in the Jazz Club. They decide to form a 3-person steering committee.
How many possible committees can be formed that do not include Fred?
Do you notice a relationship between your answers of the three parts of this problem?

rohitaop  May 18, 2018
edited by rohitaop  May 18, 2018
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A.

10 people choose 3 person committee.

\(\binom{10}{3}=120\)

B.

Since Fred is already included, all we need to do is form a two person committee.

\(\binom{9}{2}=36\)

C.

If Fred does not want to be chosen, he can be taken out of the pool.

Now it is just a nine person choosing.

\(\binom{9}{3}=84\)

The relantionship between the three answers is the sum of the answers to B and C is the answer to A.

This is because it is either Fred is on the team or not on the team. There is no other option.

Therefore, the sum of the possible committees where Fred is on and not on the team, is equal to the total amount of possible committees.

I hope this helped,

gavin

GYanggg  May 18, 2018