6 teachers and 10 students wish to join a committee, which will have 8 members. If the members are chosen at random, what is the probability that there are 4 students and 4 teachers on the committee?

Answer 1

You are choosing 8 committee members out of a total of 16 teachers and students.

You want to choose 4 students out of 10 and 4 teachers out of 6.

There are C(10,4) ways to choose 4 students out of 10.

There are C(6,4) ways to choose 4 teachers out of 6.

There are C(16,8) ways to choose 8 members out of 16.

The probability of choosing 4 students and 4 teachers is thus: C(10,4)*C(6,4)/C(16,8) = 210 *15 / 12870 = 0.245