Question

A six-member committee is formed to plan a Christmas formal. The

members of the group are to be selected from five teachers and
nine students. If the members are randomly selected, what is the
probability that it will include at least two teachers?

How do I figure out the probability!?!? :O)
HELP, PLZ! ...?

Answer 1

Total number of different committees = C(14,6) = N

We have two cases where we have less than 2 teachers.

case 1: 1 teacher (out of 5)

Number of ways to choose 1 teacher = C(5,1) = 5

Number of ways to choose the remaining members from students = C(9,5)

Total number of ways to choose a committee with exactly 1 teacher = 5C(9,5) = N1

case 2: no teacher

Number of ways to choose 6 students = C(9,6) = N2 Probability to choose at least two teachers

= (N-N1-N2)/N

=109/143

I hope tmy answer helps you