Generating all combinations

The itertools module also supports computing all combinations of a set of values. When looking at combinations, the order doesn't matter, so there are far fewer combinations than permutations. The number of combinations is often stated as

. This is the number of ways that we can take combinations of r things at a time from a universe of p items overall.

For example, there are 2,598,960 five-card poker hands. We can actually enumerate all 2 million hands by executing the following command:

hands = list(
    combinations(tuple(product(range(13), '♠♥♦♣')), 5))

More practically, assume we have a dataset with a number of variables. A common exploratory technique is to determine the correlation among all pairs of variables in a set of data. If there are v variables, then we will enumerate all variables that must be compared by executing the following command:

combinations(range(v), 2)

Let's get some sample data from http://www.tylervigen.com to show how this will work. We...