Question

A committee of 4 has to be formed among 3 economists , 4 engineers, 2 Statisticians and 1 doctor

(a) What is the probability that each of the four professions is represented on the committee

(b) What is the probability that the committee consists of the doctor and atleast one economist

(Basic Probabilty) ​

Answer 1

Answer:

There are ten people and four of them have to be chosen. That can be done in 10C4 ways = 10! / (4! * 6!) = 210 ways.

Each profession must be represented in the committee. That’s possible only if the committee of four has one economist, one engineer, one mathematician, and one doctor.

One economist from three economists can be chosen in 3C1 = 3 ways.

One engineer can be chosen from four engineers in 4C1 = 4 ways.

One mathematician can be chosen from 2 mathematicians in 2C1 = 2 ways.

One doctor can be chosen from one doctor in one way.

So, one economist, one engineer, one mathematician, and one doctor can be chosen in 3 * 4 * 2 * 1 = 24 ways.

Therefore probability of choosing a committee of four so that each profession is represented = 24 / 210 = 4/35