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a club of nine people wants to choose a board of three officers a president a vice president and a secretary how many ways are there to choose the board from the nine people now we're going to assume that some from one person can't hold more than one office that it's that if I'm picked for president that I'm no longer a valid person for Vice President or secretary so let's just think about the three different positions so you have the president you have the president you have the vice president VP and then you have the secretary secretary now let's say that we go for the president first it actually doesn't matter let's say we're picking the president slot first and we haven't appointed any of their slots yet how many possibilities are there for president well they're the club has nine people so there's nine possibilities for president there's going to be nine possibilities for president now we're going to pick one of those nine we're going to kind of take them out of the running for the other two offices right because someone's going to be President so one of the nine is going to be present there's nine possibilities but one of the nine is going to be President so you take that person aside he or she is now the president how many people are left to be vice president well now there's only eight possible candidates for vice president eight possibilities now you he or she also goes aside now how many people are left for secretary well now there's only seven possibilities for secretary so if you want to think about all of the different ways there are to choose a board for out of from the nine people there's the nine for president times the eight for vice president times the seven times the seven for secretary you didn't have to do this way it could have been you could have picked secretary first and they would have been nine choices and then you could pick vice pride in the word still been eight choice and then you could pick president last so there would have only been seven choices but either way you've got nine times eight times seven and that is let's see nine times eight nine times 8 is 72 72 times seven is two times seven is fourteen seven times seven is forty-nine plus one is 50 so 504 504 possible ways to pick your board out of a club of only nine people