SOLUTION: A committee of three people is selected at random from a set consisting of six ​teachers, three parents of​ students, and four alumni. a. What is the probability o

Algebra ->  Permutations -> SOLUTION: A committee of three people is selected at random from a set consisting of six ​teachers, three parents of​ students, and four alumni. a. What is the probability o      Log On


   



Question 1162481: A committee of three people is selected at random from a set consisting of
six ​teachers,
three parents of​ students, and
four alumni.
a. What is the probability of the event that the committee consists of all​ teachers?
b. What is the probability of the event that the committee consists of all​ parents?
c. What is the probability of the event that there will be at least 1 teacher on the​ committee?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
for 3 teachers, easiest way, if one doesn't like combinatorial notation, is (6/13) for first (5/12) for second and (4/11) for third=120/1716=0.0699
also is (6C3)/(13C3) =20/286=0.0699
for all parents it is (4C3)/(13C3)=4/286=0.0140
At least 1 teacher on committee
do it with 0 teachers on committee and then subtract from 1
(7C3)/(13C3)=35/286=0.1224. looking at a committee of all parents or alumni
so the answer with at least 1 teacher is 1-0.1224 or 0.8776.