Question

Five people are selected to make up a committee.If there are 5 students,6 parents and 6 village leaders. Find the probability that 2 students are in the committee?

Answer 1

if 2 students are in committee, then we have to choose 3 people from 6 parents and 6 village leaders. So, number of ways to choose 2 students in the committee:

$n=C^3_{12}=\frac{12!}{9!3!}=220$

total number of ways to choose 5 people in the committee:

$N=C^5_{17}=\frac{17!}{12!5!}=6188$

the probability that 2 students are in the committee:

$P=\frac{n}{N}=\frac{220}{6188}=\frac{55}{1547}$