7 freshmen 8 sophomores 6 juniors and 10 seniors are eligibl

7 freshmen, 8 sophomores, 6 juniors, and 10 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors?
Round your answer to 6 decimal places

Solution

7 freshmen, 8 sophomores, 6 juniors, and 10 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors

total = 7+8+6+10 = 31

Total selection = 31C14

Now choosing 2 freshmen = 7C2

3 sophomores = 8C3

4 juniors = 6C4

5 seniors = 10C5

So, Probablity = (7C2*8C3*6C4*10C5)/ 31C14

=(21*56*15*252)/265182525

=0.0167631