Question

There are six democrats and five republicans on a senate committee. A Committee consisting of four people must be formed.

(a) In how many ways can a committee of four people be formed?

(b)In how many ways can two democrats and two republican be chosen?

(c) What is the probability that two democrats and two republican will be chosen?

Answer 1

a) Total members = 6 + 5 = 11

We need to select 4

So, Total ways = C(11,4)

So, there are 330 committees of four people can be formed.

b) Total ways to select 2 democrates and 2 republican = C(6, 2)*C(5, 2)

So, there are total 150 ways.

c) P = 150/330 = 5/11

So, 5/11 is the probability of selecting 2 democrats and 2 republicans.

Please comment if any doubt. Thank you.