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Combinations - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

We're now going to look at the number of different ways to select three students from a class of 20 and what I see is that we're trying to select three kids and it doesn't say anything about the order we're choosing them, so no matter what three kids we choose it's always going to be the same. So if we choose student a, b and c it's the same exact selection as we choose c, b, a, it's just the final three, which tells me we're going to be doing a choosing operation.

Basically all we do is the number of students in the entire class 20 choose the number of students that we are concerned with which is just going to be 3. I do want to talk about another way we could actually write question. This turns into being 20 factorial over 20 minus 3 factorial, 17 factorial times 3 factorial.

The other way we could actually do this is say you're choosing the students that you don't want to select and so if we said 20 choose 17, we actually get the exact same answer, what this turns into is 20 factorial divided by 20 minus 17 factorial, which is 3 factorial over 17 factorial.

So when choosing order doesn't matter quite as much because basically if you choose the people you want or you choose the people you don't want, you're going to end up with the exact same thing.

Typically again it's easier just to look at and say okay 20 choose the number that you're dealing with, but the lucky thing about choosing is if you do it backwards, you still end up with the right answer.

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