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elimination problem

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elimination problem

by mehaksal » Thu Aug 30, 2012 6:51 am
A community of 3 people is to be selected from 5 married couples, such that the community does not include two people who are married to each other. How many such communities are possible?

to count cases in which a couple is included, is 5C2 * 8C2 the correct way?
then I can subtract it from 10C3
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by neelgandham » Thu Aug 30, 2012 8:09 am
Please find my solution here - https://www.beatthegmat.com/married-couple-t95696.html
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by adthedaddy » Thu Aug 30, 2012 8:12 am
Hi mehaksal, this can be solved as follows -

Logic:
Communities without a couple = [Total Combinations (comunities)] - [combinations (communities) where a couple is together]
Total 3 member communities out of 10 people = 10C3 = 120
Combinations where couple is together = 5C1*8C1 = 5*8 = 40 (because 5C1 indicates selection of one couple which includes 2 people; the remaing person can be any one from the remaining 8 left after selection of the 2 persons married to each other)

Reqd = 120 - 40 = 80

Hope this clarifies :-)
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