Question 1081869: A football team consists of 19 each freshmen and sophomores, 14 juniors, and 17 seniors. Four players are selected at random to serve as captains. Find the probability that:
a)all 4 are seniors
b)There is one of each: freshman, sophomore, junior , and senior
c)There are 2 sophomores and 2 freshmen
d)At least one of the students is a senior
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 69C4 are the number of ways (864,501)
17C4 are all seniors, and probability is 0.0028m dividing 2380 by 864,501.
one of each is a numerator of 19C1*19C1*14C1*17C1=85918, probability is 0.0994.
2 sophomores and 2 freshmen are 19C2*19C2=29241 and probability is 0.0338
at least one is a senior is 1-no seniors, and no seniors has a numerator of 52C4. That probability is 0.3132.
Therefore at least one senior is the complement or 0.6868.
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