Combinatorial Calculator

Calculate the number of ways to select r items out of n items.

Instructions

Enter the total number of elements, n, and the number of elements to choose, r, along with whether order matters (combinations vs permutations) and whether items can be selected more than once (replacement or repetition) to calculate the number of permutations or combinations.

nCr Calculation

The number of combinations of a set (also denoted as nCr) is the number of ways r items can be combined (order does not matter) from a set of size n.

With Replacement

$$( nCr = \frac{(r + n - 1)!}{r! \times (n - 1)!})$$

Without Replacement

$$( nCr = \frac{n!}{r! × (n - r)!})$$

nPr Calculation

The number of permutations of a set (also denoted as nPr) is the number of ways r items can be ordered from a set of size n.

With Replacement

$$( nPr = n^r)$$

Without Replacement

$$( nPr = \frac{n!}{(n - r)!})$$