Question

A student faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random: a. two students and two faculty members and b. one faculty member and three students. ...?

Answer 1

A.) Probability of selecting two students and two faculty members from 20 students and 5 faculty volunteers = no of ways of selecting two students and two faculty members from 20 students and 5 faculty volunteers divided by the number of ways of selecting 4 people from 25 people = (20C2 x 5C2) / 25C5 = 1900 / 53130 = 0.036 = 3.58%

b.) Probability of selecting three students and one faculty members from 20 students and 5 faculty volunteers = no of ways of selecting three students and one faculty members from 20 students and 5 faculty volunteers divided by the number of ways of selecting 4 people from 25 people = (20C3 x 5C1) / 25C5 = 5700 / 53130 = 0.107 = 10.7%