subh2273 wrote:A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be fo from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple?
(A)
105
(B)
207
(C)
210
(D)
540
(E)
5,040
Good committees = total committees - bad committees.
Total committees:
From 10 people, the number of ways to choose 4 = 10C4 = (10*9*8*7)/(4*3*2*1) = 210.
Bad committees:
Since a good committee includes at most 1 married couple, a bad committee is composed of 2 married couples.
From 3 married couples, the number of ways to choose 2 to form a 4-member committee = 3C2 = (3*2)/(2*1) = 3.
Thus:
Good committees = 210-3 = 207.
The correct answer is
B.
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