CAT 2

[ahistegt]

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?

20%
30%
40%
50%
60%

Although I got this question right, I couldn't quite follow the explanation provided in the exercise.

[kylo]

total no of subcommittees = 6C3 = 40.

total no of subcommittees with Michael & Anthony = 4.

% = 4/40 = 10%.

dont know where i m going wrong.


Thanks!

[michael_shaunn]

HI KYLO,
YOU HAVE DONE EVERYTHING RIGHT AS I PRESUME............EXCEPT THAT 6C3 IS 20 AND NOT 40.
SO,I BELEIVE THAT THE ANSWER SHOULD BE 20%.

[JonathanSchneider]

Nice catch, Michael, but there's actually one piece that we still need to add. We are not asked what % of ALL subcomittees contain both people, but rather what % of subcomittees that ALREADY include Michael will also include Anthony. The number of subcomittees that include Michael is actually 5c2, or 10, because Michael is guaranteed a seat. The answer is thus 4/10, or 40%.

An easier approach is to simplify the logic here. Each person has an equal chance of being on any comittee. Michael must be on a committee. This leaves five empty seats, two of which are on his comittee and three of which are not. Anthony could be placed anywhere, with an equal chance for any seat. His options are thus 2/5, or 40%. Be on the lookout for ways to radically simplify the steps you need to take when doing problems of this type.