Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 threeperson subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
OA C
Source: Manhattan Prep
Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2
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We can think of this as a probability question: What is the probability that Anthony and Michael are on the same subcommittee?BTGmoderatorDC wrote: ↑Thu Jun 02, 2022 10:50 pmAnthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 threeperson subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
OA C
Source: Manhattan Prep
Now, assume that we're creating subcommittees.
We want to place 6 people in the following spaces:
_ _ _  _ _ _
First, we place Michael in one subcommittee; it makes no difference which one:
M _ _  _ _ _
When we go to place Anthony, we see that there are 5 spaces remaining.
2 spaces are on the same subcommittee as Michael.
So the probability that they are on the same subcommittee is 2/5 = 40%
Answer: C