SOLUTION: A class has 4 seniors, 5 juniors, 3 sophomores, and 6 freshmen. If you randomly choose 6 students, what is the probability that: a. You choose at least 2 seniors? b. You ch

Question 1166385: A class has 4 seniors, 5 juniors, 3 sophomores, and 6 freshmen. If you randomly choose
6 students, what is the probability that:
a. You choose at least 2 seniors?
b. You choose exactly 3 juniors and 3 freshman
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
at least 2 seniors is 1-prob (1 senior) and prob (0 seniors)
denominator is 18C6 and that is 18564
the numerator for the first (1 senior) is (4C1)(14C5) since the other classes are not fixed.
this is 4*2002 or 8008
the numerators for 0 seniors is 14C6 and that is 3003
so the probability of at least 2 seniors is 1-(11011)/18564=0.4069
Can check with 2, 3 or 4 seniors. for 3 it is 4C3 *14C3=1456 ways
for 4 seniors it is 4C4*14C2=1*91=91
for 2 seniors it is 4C2*14C4=6006
that sum decided by 18564 gives a probability of 0.4069.

for b the numerator is 5C3*6C3 and that is 10*20=200
the probability is 0.0108

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