# Ways to pickÂ officers

## Video transcript

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
one person can't hold more than one office. That if I'm picked for
President, then 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 Vice President, VP, and then you have
the Secretary. Now, let's say that we go for
the President first. It actually doesn't matter. Let's say we were picking the
President slot first and we haven't appointed any
other slots yet. How many possibilities are
there for President? Well, 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 President. 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 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 from
the nine people, there's the 9 for President times the 8
for Vice President times the 7 for Secretary. You didn't have to
do it this way. It could've been-- you could've
picked Secretary first. Then there would've
been nine choices. And then you could've picked
Vice President, and there would've still been
eight choices. And then you could've picked
President last, and there would've only been
seven choices. But either way you would've
got 9 times 8 times 7. And that is, let's see, 9 times
8 is 72 times 7 is-- 2 times 7 is 14, 7 times
7 is 49 plus 1 is 50. So 504 possible ways to pick
your board out of a club of only nine people.