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Permutations and Combinations

Permutations and combinations is the math of counting how many ways you can arrange or choose items from a group.

Think of it this way

You have three jars on a shelf. You can fill them with a red, a blue, and a green ball. The order matters — red-blue-green is a different setup than blue-red-green. That is a permutation. A combination only counts which balls you picked, not which jar holds which.

Explaining permutations and combinations by grade level

Think about making change with coins. You pick a few coins from your pile. The coins you pick matter, but not the order you grab them. Now line those same coins up in a row. Change the order and you get a new line. Picking is one thing. Ordering is another.

Projects that explore permutations and combinations

Coin Change Combinations and Fast Algorithms

When order does not matter, combinations count the different ways you can choose items from a group. Making change for a dollar means picking coins that add up correctly — and it turns out there are exactly 292 ways to do it using pennies, nickels, dimes, quarters, and half-dollars. That number comes from testing every possible mix of the five U.S. coins, which a computer program can do through brute force. As a result, each solution is a different combination of those five coin types.

Hard