dvalenz wrote:IF a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
20
50
50
80
120
Number of options for the first person = 10. (Any of the 10 people.)
Number of options for the second person = 8. (Of the 9 remaining people, anyone but the spouse of the first person selected.)
Number of options for the third person = 6. (Of the 8 remaining people, anyone but the spouses of the first two people selected.)
To combine these options, we multiply:
10*8*6.
Since the ORDER of the selections doesn't matter -- ABC is the same committee as BCA -- we divide by the number of ways to ARRANGE the 3 people selected (3!):
(10*8*6)/(3*2*1) = 80.
The correct answer is
D.
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