venmic wrote: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%
40
Please i need a easy approach to this
Thx
let member be a,b,c,d,e,f; total no. of ways of selecting 3 members be 6C3;= 20;
if we observe we will notice that whenever we select first members of a group last three are selected automatically, for example; if we selecte abc, def are selected automatically, and if we select def, abc is formed automatically, and since def,abc is similar as abc,def i.e. we have counted our group twice, so we need to halved the total no. of ways of selecting the group= 1/2*20=10;
since micheal and anthony will always be together, their third partner can be selected from any of the remaining 4 members in 4C1 ways= 4; i.e. out of 10 committees,or groups that are form 4 contains anthony and micheal as its members hence required percentage= (4/10)*100=40% hence
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