Choosing a Counting Model

Before using a permutation or combination formula, decide what makes two outcomes different.

Ask two questions:

1. Does order matter? If AB and BA represent different outcomes, order matters.
2. Can an item be reused? Repetition changes the model and the count.

For selecting r distinct items from n distinct items without repetition:

• order matters: P(n,r) = n!/(n-r)!;
• order does not matter: C(n,r) = n!/[r!(n-r)!].

If each of r positions can independently use any of n choices, the count is nʳ.

The Counting Explorer keeps counts as exact integers even when they exceed JavaScript’s ordinary safe-integer range.