SOLUTION: A CLUB HAS 30 FRESHMEN, 25 SOPHOMORES, 40 JUNIORS. 6 ARE CHOSEN AT RANDOM, WHATS THE PROBABILITY THAT 2 OF EACH ARE CHOSEN.

Question 927825: A CLUB HAS 30 FRESHMEN, 25 SOPHOMORES, 40 JUNIORS. 6 ARE CHOSEN AT RANDOM, WHATS THE PROBABILITY THAT 2 OF EACH ARE CHOSEN.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
club members.
From all the club members,
different groups of 6 can be made.
How many of those groups include 2 freshmen, 2 sophomores and 2 juniors?
How many different groups of 6 can be made, including 2 freshmen, 2 sophomores and 2 juniors?
There are ways to choose a group of 2 freshmen out of the 30 freshmen in the club.
There are ways to choose a group of 2 sophomores out of the 25 sophomores in the club.
There are ways to choose a group of 2 juniors out of the 40 juniors in the club.
So, there are different groups of 6 than can be made, including 2 freshmen, 2 sophomores and 2 juniors.
As a fraction of all the groups of 6 that can be made, that is
,
and, as any group is as likely as any other group,
that is the probability that the randomly chosen group of 6 will contain exactly 2 students from each class.
(rounded)
You could say that the probability of such a group is 11.7%.
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