If you have 5 women and 7 men and you want to choose a commitee of size 5 consisting of 2 women and 3 men then i get that there are 5 choose 2 ways of selecting a group of 2 from 5 and 7 choose 3 ways of selecting a group of 3 from 7 and then by the basic principle of counting you just multiply these.
But what if two men refuse two work together apparently then a total of 2 choose 2 times 5 choose 1 = 5 groups out of the total of 35 are no longer possible but i dont see how they done this.
appreciate any help, thanks
If 2 men refuse to work together, then the groups that are ruled out are the ones including that pair - which are that pair + one other man. Since there are 7-2=5 other men that could complete the group, 5 out of the 35 groups of 3 men are no longer possible