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Please excuse this simple question, but I cannot seem to find an answer. I'm not very experienced with math, but I keep seeing a notation that I would like explained. The notation I am referring too generally is one variable m floating over another variable n enclosed in paraentheses. You can see an example in the first equation here.

What does this mean? Thanks in advance for the help.

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marked as duplicate by J. M., Davide Giraudo, Amzoti, vonbrand, Dennis Gulko Apr 8 '13 at 18:32

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

up vote 7 down vote accepted

That notation is read "$n$ choose $m$", and it indicates the number of ways one can choose $m$ objects from a collection of $n$ objects, if we don't care about "order". Think about a bag of 10 many different ways can I pick 5 objects out of the bag? That number is $\binom{10}{5}$.

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Thanks for the clear explanation! – turtle Dec 2 '12 at 23:56

That is a binomial coefficient. $\binom{n}{m}$ means the number of subsets of size $m$ of a fixed set of size $n$.

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This is called the binomial coefficent, often read "n choose m", since it provides a way of computing the number of ways to choose $m$ items from a collection of $n$ items, provided the order or arrangement of those items doesn't matter.

To compute the binomial coefficient: $\displaystyle \binom{n}{m}$, you can use the factorial formula: $$\binom{n}{m} = \binom{n}{n-m}=\frac{n!}{m!(n-m)!}$$

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