Order is Not Important
Combinations problems are very similar to permutations problems. The key distinction is that, unlike permutations, arrangement or order doesn’t matter for combinations.
A combination is a selection of objects or elements from a group where order is not relevant. Combination questions ask how many selections or subsets there are. For example, if a committee is being selected and there will be a president, vice president, and treasurer, then order matters so it is a permutation problem. But if a committee of three people is being formed without specific roles, then order does not matter and it is a combination problem.
Permutation vs. Combination
The two examples below use very similar dice games, but a slight difference means one uses permutations, and the other uses combinations. The comparison illustrates the difference between permutations and combinations.
In a game of dice, you roll one red die and one blue die and record the results. If you roll “doubles” (both dice land on the same face), the results aren’t counted and you roll again. How many permutations are possible for one roll?