Question

a committee of 5 ppl is to be chosen from the following department. 4 faculty members in CS and enginerring, 5 in electrical engineering, 6 in mechanical engineering, and 3 aerospace engineering.

a) how many committees are possible?

B) how many committees with at least 2 faculty members from CSE?

Answer 1

A.

Total # of people = 4+5+6+3 = 18

Now from 18 people, we need to select 5 people for committee.

This can be done in C(18, 5) ways = 8568

So total number of ways of forming committee = 8568

B.

First let's select 2 faculty from a group of 4. This can be done in C(4, 2) = 6

Now we are left with 16 people and we need to select 3 from it. This can be done in C(16, 3) ways = 560

So total different committee possible = 6*560 = 3360

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