sana.noor wrote:here is another similar question
"If a committee of 4 people is to be selected from among 6 married couples so that the
committee includes exactly two people who are married to each other, how many such
committees are possible?"
now what should be the answer to this question, my answer is 60
One married couple must be combined with one unmarried couple.
Married couple:
Number of options = 6.
Unmarried couple:
Once the married couple has been selected, 10 people remain.
From these 10 people, we must choose 2 who are unmarried.
Number of options for the first person selected = 10.
Number of options for the second person selected = 8. (Of the 9 remaining people, anyone but the first person's spouse.)
To combine these options, we multiply:
10*8.
Since the ORDER of the two people doesn't matter -- AB is same couple as BA -- we divide by the number of ways to ARRANGE the 2 people (2!):
(10*8)/(2*1) = 40.
To combine our options for each type of couple, we multiply the results above:
6*40 = 240.
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