Question 1103356
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Okay; I will use different numbers: 4 freshmen, 3 sophomores, 7 juniors, and 7 seniors.  And we will still make a committee of 14 with 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors.<br>
The basic definition of probability says that the answer is
(number of ways of choosing 2 of the 4 freshmen AND 3 of the 3 sophomores AND 4 of the 7 juniors AND 5 of the 7 seniors) divided by (the total number of ways of choosing 14 of the total 21 students).<br>
Because the calculations involve choosing among candidates, you will be using the "n choose r" concept repeatedly.  Since you are asking this question, I will assume you are familiar with that concept.<br>
The denominator of our probability fraction is the number of ways of choosing 14 of the 21 students: C(21,14).<br>
For the numerator, we have to choose certain numbers of each of the four class levels.  So the numerator of the probability fraction will be C(4,2)*C(3,3)*C(7,4)*C(7,5).<br>
C(21,14) = 116280; C(4,2)*C(3,3)*C(7,4)*C(7,5) = 6*1*35*21 = 4410; the probability that the committee has 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors is {{{4410/116280 = .0379}}} to 4 decimal places.<br>
Obviously the process for solving your example will be the same, just with different numbers.