A committe of 5 members will be chosen from a group of 10 teachers and 5 students. What is the probability that the committee

Question

will have
A) all teachers?
B) 3 teachers and 2 students?
C) 3 or 4 teachers?

Answer 1

all you have to do is figure out the probability of each and multiply appropriately.

a) the teachers represent 10/15 or 2/3 of the candidates, we need 5 teachers. imagine someone choosing commitee members randomly. they would have a 2/3 chance of picking the first teacher, a 9/14 chance of picking the second teacher, (there are now 14 candidates and 9 teachers), a 8/13 chance of picking the third teacher, a 7/12 chance of picking the fourth teacher, and a 6/11 chance of picking the fifth teacher.
We now multiply.
(2/3)*(9/14)*(8/13)*(7/12)*(6/11)