Question

A committee of 3 is being formed randomly from the employees at a school: 6 administrators, 36 teachers and 5 staff. what is the probability that all 3 members are administrators? express your answer as a fraction

Answer 1

A committee of 3 is being formed randomly from the employees at a school: 6 administrators, 36 teachers, and 5 staff. what is the probability that all 3 members are administrators? express your answer as a fraction

step 1

Find out the total possible results

Calculate the combination 47C3

`47C3=(47!)/(3!(47-3)!)=16,215`

step 2

Calculate the combination 6C3 (administrators)

`6C3=(6!)/(3!(6-3)!)=20`

therefore

the probability is

P=20/16,215

simplify

P=4/3,243