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Previously, we looked at how to calculate a binomial coefficient (to find the total number of possible combinations) and an example of how to generate a list of combinations with hard-coded loops.

A function would be much more useful to us if it was flexible - if it could generate a list of combinations for any size set of numbers. We can’t do this with the hard coded loop solution, so we need to come up with a better method.
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In statistics and probability, the combination is something special. There are tons of problems that revolve around how many combinations you can get choosing a certain number of random items from a set.

We’ve developed mathematical formulas to help us determine the number of possible combinations - and therefore the possibility of getting any single combination - but how can we generate a list of the actual combinations?
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I came across this problem on the DigitalPoint forums the other day. How can we write a script to calculate the total number of random combinations in a set (i.e. the binomial coefficient), and how can we generate a list of these combinations?

Today, we’ll tackle the first part. We’ll start with a quick primer on math - what is a binomial coefficient? Then, we’ll look into the most efficient way to calculate that and get the total number of possible combinations.
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