Since the 6 people are being split into two 3-member committees, we know that Michael will serve on a committee.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%
The only question is whether Anthony will be among the pair of people chosen to serve with Michael.
Total number of pairs that can be formed from the 5 people aside from Michael = 5C2 = 10.
Total number of people (aside from Michael) that could be combined with Anthony to form a pair = 4.
(Pairs with Anthony)/(total possible pairs) = 4/10 = 40%.
The correct answer is C.
Another approach:
P(1st person chosen to serve with Michael is NOT Anthony) = 4/5.
P(2nd person chosen to serve with Michael is NOT Anthony) = 3/4.
Thus, P(Anthony is NOT chosen to serve with Michael) = 4/5 * 3/4 = 3/5.
Thus, P(Anthony IS chosen to served with Michael) = 1 - 3/5 = 2/5 = 40%.
