Question

A committee of 3 is being formed randomly from the employees at a school: 4 administrators, 30 teachers and 4 staff. what is the probability that all 3 members are teachers? express your answer as a fraction.

Answer 1

There are in all 38 (4 + 30 + 4) people.

Probability = (No. of Favourable possibilities) / (No. of All possibilities)

We have to select 3 members out of 38, so, number of all possibilities:

(38x37x36)/(3x2x1) = 8436.

3 teachers could be selected out of 30 teachers, so, number of favourable possibilities:

(30x29x28)/(3x2x1) = 4060.

Therefore the required probability is:

4060/8436 = 1015/2109 = 48%