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Combinations - Concept

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!

Permutations and combinations occur when we are trying to find the probability of a certain event happening. When working with statistics combinations, we are trying to find the number of possible combinations within a set. Therefore, when working with statistics combinations, the order of events does not matter.

Now we're going to look at the number of different ways to select 3 students from a class of 20. And what I see is that we're trying to select 3 kids and it doesnÂ’t say anything about the order we're choosing them, so no matter what 3 kids we chose it's always going to be the same. So if we chose student a, b and c it's the same exact selection as if we chose c, b, a okay it's just the final 3. 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 okay. I do want to talk about another we could actually write this question, this turns into being 20 factorial over 20 minus 3 factorial, 17 factorial times 3 factorial.
The other we could actually do this is say you're choosing these students that you donÂ’t want to select okay 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 is 3 factorial over 17 factorial. So a choosing order doesnÂ’t matter quite as much because basically if you choose the people you want or you choose the people you dnÂ’t want you're going to end up with the exact same thing okay.
Typically you're going just it's easier just to look out and say okay 20 choose the number that you're dealing with but lucky thing about choosing is if you do it backwards you still end up with the right answer.

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