Question 169665: A club consists of 25 married couples. Determine how many ways a committee of 7 people can be formed from these couples if
a) there are no restrictions?
b) there are exactly 5 men on the committe?
c) at least one person must be a man?
d)there must be at least 3 women and at least 2 men?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A club consists of 25 married couples. Determine how many ways a committee of 7 people can be formed from these couples if
a) there are no restrictions?
Ans:
50C7 = 99,884,400
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b) there are exactly 5 men on the committee?
Ans:
25C5 * 25C2 = 53130*300 = 15,939,000
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c) at least one person must be a man?
# with NO men is 25C7 = 480,700
So, # with at least one man is 50C7-480,700 = 99,403,700
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d)there must be at least 3 women and at least 2 men?
That's pretty messy so I'll leave that to you.
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Cheers,
Stan H.
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