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?

Answer 1

Teacher = T, Student = S
(5T,1S) + (4T,2S) + (3T,3S) + (2T,4S)
now find probability of each and add them up

Answer 2

That is the part i knew how to do lol what is the probability equation?

Answer 3

P(at least 2 teachers)=1-P(0 teachers)-P(1 teacher)

There are 14C6 ways to a committee of 6 from 14.

P(no teachers)=(9C6)(5C0)/(14C6)
P(1 teacher)=(9C5)(5C1)/(14C6)

So

P(at least 2 teachers)=1-(9C6)(5C0)/(14C6)-(9C5)(5C1)/(14C6)

=2289/3003=about 0.7622 or 76.22%