Question 169722: 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 committee
c) at least one person must be a man
d) there must be at least 3 women and at least 2 men
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! a)50C7=50!/((50-7)!*7!)=99,884,400
.
b)25C5 * 25C2 =53130 * 300 = 15,939,000
.
c)99,884,400-(25C7*25C0)
=99884400-480700
=99,403,700
.
d)50C7-2(25C7)-2(25C6*25C1)-(25C5*25C2)
=99884400-961400-8855000-15939000
=74,129,000
.
Ed
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