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Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-

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by BTGModeratorVI » Wed Dec 16, 2020 12:49 pm

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Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%

Answer: C
Source: Princeton Review
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Source: — Problem Solving |

After selecting Micheal, the number of possible committees can be found by considering 5 remaining pool of candidates.
Out of all the 5 candidates, Anthony can occupy any of the 2 positions remaining to fill up Micheal's subcommittee.
Therefore, the possibility of having a subcommittee that includes Micheal and Anthony = 2/5
And if 5 = 100%
$$Then\ 2\ will\ yield=\frac{100\cdot2}{5}=40\%\ \ \ $$
Answer = option C
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