a choice subcommittee

[rohilla_sandeep]

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%

The correct answer is 40 %
In the explanation
As an alternate method, imagine splitting the original six-person board into two equal groups of three. Michael is automatically in one of those groups of three. Now, Anthony could occupy any one of the other 5 positions -- the 2 on Michael's committee and the 3 on the other committee. Since that probability must correspond to the ratio of committees asked for in the problem, the answer is achieved.

Here the explanation seems ambiguous as the problem is considered as permutation rather than combination. Shouldn't it be : Let us consider M & A both are in one committee then the 3rd person can be selected out of remaning 4 by 4c1 = 4 ways.
and the total ways in which two committee can be formed is 6c3 = 20 ways. Therefore , probality % is = 4/20 * 100 = 20 %

[jnelson0612]

rohilla, check out this thread for a lot of discussion: anthony-and-michael-sit-on-the-six-member-t9526.html