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# A group consists of 17 men and 22 women. How many pairs can

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A group consists of 17 men and 22 women. How many pairs can [#permalink]

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07 Nov 2004, 16:29
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A group consists of 17 men and 22 women. How many pairs can be made to contain at least one woman?
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Paul

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Joined: 07 Nov 2004
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07 Nov 2004, 16:41
# of ways to choose 1 man and 1 woman = 17C1*22C1=374
# of ways to choose 0 man and 2 women = 17C0*22C2= 231

answer = 374+231 = 605

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07 Nov 2004, 19:15
Do we consider each man and woman a unique identity in such a question?

If this is not the case then the solution will be simply 19

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GMAT Club Legend
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07 Nov 2004, 19:46
Do we consider each man and woman a unique identity in such a question?

If this is not the case then the solution will be simply 19

How can a person not be unique
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Paul

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07 Nov 2004, 20:10
17C1*22C1 + 17C0*22C2 = whatever this may be.

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Joined: 31 Dec 1969

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Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

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08 Nov 2004, 04:44
To find the no. of pairs consisting of atleast 1 women, find total possible no. of pairs i.e. (39C2) and subtract it from the total no of pairs that are both males. i.e. (17C2)

Hence the answer is 39C2 - 17C2 = 741 - 136 = 605

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Subhen

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08 Nov 2004, 13:53
We can have a pair of two women or 1 man and 1 woman.
2 women can be selected in 22C2 ways=231
and 1 man and woman in 17C1*22C1 ways=374

total combination= 231+374=605.
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GMAT Club Legend
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08 Nov 2004, 20:48
OA is 605
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Paul

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08 Nov 2004, 20:48
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# A group consists of 17 men and 22 women. How many pairs can

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