How to Do Combinations in Math

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Combinations have a certain formula that you need to think about when completing these types of math problems. Learn how to do combinations in math with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Principles of Math
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to do combinations in Math. Now, a combinations have a certain formula that you have to think about writing, but once you have, understand the formula how it works, you can just plug your numbers and go from there. So, here's the combinations formula. So, in combinations which is use in probability theory and counting scenarios, it's nCr. N and r are kind of like subscripts here and basically, n is the total amount of objects that you have to choose from and r is the number of objects taken from the total. And the idea here is r is never larger than n. So, if you have the formula, it's going to be n factorial in the numerator divided by, now, there's going to be two parts in the denominator, r factorial as well as n minus r factorial. Now, the important thing to think about here is you have to figure out what the expression inside the parenthesis is first, you cannot distribute the factorial symbol. A lot of folks like to do that, it just cannot be done. So, if you have 10C3, that means if you have ten objects and you're taking three of them at a time and order is not important, that's the other thing to remember about combinations, basically the idea here is ten is going to replace the n and three is going to replace the r. So, you have ten factorial over, r is three, so three factorial times n is ten minus r is three factorial. So again, you have to think about what's in the parenthesis first, ten minus three is seven; it's going to be ten factorial over three factorial, seven factorial. Now, you can either do this by hand, by expanding the factorials and then do the cancellations or if you're going to do this on a calculator that's fine too and some calculators even have a combination function depending on how advance your calculator is. But, this is the formula and you should be able to go from there once you know what numbers to plug in. So, I'm Jimmy Chang and that's how to do combinations in Math.


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