Question

A committee of 4 is being formed randomly from the employees at a school: 4 administrators, 32 teachers and 5 staff. what is the probability that all 4 members are teachers? express your answer as a fraction

Answer 1

A committee of 4 is being formed randomly from the employees at a school: 4 administrators, 32 teachers, and 5 staff. what is the probability that all 4 members are teachers? express your answer as a fraction

step 1

Find out the total posible results

Find out the combination 41C4

$41C4=\frac{41!}{4!\cdot(41-4)!}=101,270$

step 2

Find out the combination 32C4

$32C4=\frac{32!}{4!\cdot(32-4)!}=35,960$

therefore

the probability is

P=35,960/101,270

in simplest form

P=3,596/10,127