Question 1061789: A committee consists of a President, a Vice President, a Treasurer, and a Secretary. The posts are to be drawn from 30 people (7 males, 23 females), and it allows a person to hold more than one post, provided that one of them is not a President.
In how many ways can this committee be organized?
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! First of all, one and only one person can be President--and that person can hold no other office, so that gives you 30 possibilities. Then you have 29 people, who can individually hold the other 3 offices, so that gives you 30x29, or 870 possibilities. Then you have 29 people combined 2 at a time, since one person can hold 2 separate offices, which gives you 870 x 812, or 706,440 combinations. Finally you have 29 people combined 3 at a time, with each person holding just one office, which gives you 706,440 x 21,924, or 15,487,990,560 different possibilities!!!!!!
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