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by maihuna » Tue Mar 15, 2011 12:10 pm
A committee of three people is to be chosen from the president
and vice president of four di¤erent companies. What is the
number of di¤erent committees that can be chosen if two
people who work for the same company cannot both serve
on the committee?
(A) 16
(B) 24
(C) 28
(D) 32
(E) 40
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by anshumishra » Tue Mar 15, 2011 1:28 pm
maihuna wrote:A committee of three people is to be chosen from the president
and vice president of four di¤erent companies. What is the
number of di¤erent committees that can be chosen if two
people who work for the same company cannot both serve
on the committee?
(A) 16
(B) 24
(C) 28
(D) 32
(E) 40

No. of ways to select any 3 candidates from 8 (4 P + 4VP) =
8C3 = 6*7*8/2*3 = 56

No. of ways to select 3 candidates with at least 1 pair (P+VP) from the same company = 4C1(select 1 out of 4 pairs)*6(select any candidate out of 6 left) = 24

So, required no. of ways = 56-24 = 32
D
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