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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

User Javier Holguera
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1 Answer

21 votes
21 votes

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=(41!)/(4!\cdot(41-4)!)=101,270

step 2

Find out the combination 32C4


32C4=(32!)/(4!\cdot(32-4)!)=35,960

therefore

the probability is

P=35,960/101,270

in simplest form

P=3,596/10,127

User BARNZ
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