SOLUTION: A group of 10 people consists of 5 men and 5 women. A committee of 4 is chosen from this group. What is the probability that one or more of the committee members is a man?

Question 264403: A group of 10 people consists of 5 men and 5 women. A committee of 4 is chosen from this group. What is the probability that one or more of the committee members is a man?
Found 2 solutions by stanbon, drk:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A group of 10 people consists of 5 men and 5 women. A committee of 4 is chosen from this group. What is the probability that one or more of the committee members is a man?
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P(at least one man) = 1 - P(no man)
= 1 - [5C0]/10C5]
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Cheers,
Stan H.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
It would be easier to say 1 - P(0 men).
So, of the 4 men we need 0 men
and of the 4 women, we want 4 women
in combinations, we get
(5c0)(5c4) /(10c4)
this is
(1)(5) / 210
and reduced get
1/42, but we need 1 - this or
1 - 1/42 = 41/42
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