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
[tex]47C3=\frac{47!}{3!(47-3)!}=16,215[/tex]step 2
Calculate the combination 6C3 (administrators)
[tex]6C3=\frac{6!}{3!(6-3)!}=20[/tex]therefore
the probability is
P=20/16,215
simplify
