Probability Question

Question

In an office, there are three secretaries, four accountants, and two receptionists. If a committee of three is to be formed, find the probability that one of each will be selected.

Answer 1

There are 9 people total (3 secretaries, 4 accountants, and 2 receptionists).

We want to select 3 people to be in the committee.

C(9, 3) = 9!/(3!*6!) = 84 ways to choose 3 people to be in the committee

C(3, 1) = 3 ways to choose a secretary to be in the committee

C(4, 1) = 4 ways to choose an accountant to be in the committee

C(2, 1) = 2 ways to choose a receptionist to be in the committee

P(selecting 3 people) = (3*4*2)/84 = 24/84 = 0.2857

The probability of selecting 3 people (one from each group) to be in the committee is about 0.2857.