Anthony and Michael sit on the six member board od directors for compnay 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?
Pick one
A) 20%	B) 30%	C) 40%	D) 50%	E) 60%
First approach:   Let's take the group with Michael: there is a place for two other members and one of them should be taken by Anthony, as there are total of 5 people left, hence there is probability of 2/5=40%.   Second approach:   Again in Michael's group 2 places are left, # of selections of 2 out of 5 5C2=10 - total # of outcomes.   Select Anthony - 1C1=1, select any third member out of 4 - 4C1=4, total # =1C1*4C1=4 - total # of winning outcomes.   P=# of winning outcomes/# of outcomes=4/10=40%   Third approach:   Michael's group:   Select Anthony as a second member out of 5 - 1/5 and any other as a third one out of 4 left 4/4, total=1/5*4/4=1/5;   Select any member but Anthony as second member out of 5 - 4/5 and Anthony as a third out of 4 left 1/4, total=4/5*1/4=1/5;   Sum=1/5+1/5=2/5=40%   Fourth approach:   Total # of splitting group of 6 into two groups of 3: 640%3*340%3/2!=10   # of groups with Michael and Anthony: 140%1*140%1*440%1=4   P=4/10=40%   Answer: 40%.
<result>C</result>
Anthony and Michael sit on the six member board od directors for compnay 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?