Permutation and Combination Calculator

A permutation and combination calculator is a counting tool that helps you solve nPr and nCr problems quickly. It is useful when you want to know how many possible arrangements or selections can be made from a larger set of items.

In probability, statistics, combinatorics, exams, and everyday counting problems, these formulas appear often. Instead of working through factorial expressions by hand, you can enter n and r to get the result instantly.

First, identify the total number of available items, which is n. Then identify how many items are being selected, which is r. The key question is whether order matters in the final result.

If order matters, use the permutation formula nPr. If order does not matter, use the combination formula nCr. This calculator applies the correct formula automatically after you choose the calculation type.

Permutations are used when the arrangement itself matters. For example, if you are awarding first, second, and third place, the order of winners changes the outcome, so permutation is the correct method.

Other examples include arranging books on a shelf, setting passwords from selected characters, assigning seats, ranking contestants, or assigning different roles from the same group of people.

Combinations are used when you only care which items are chosen, not the order in which they appear. For example, choosing 3 students for a committee uses combinations because the same group counts only once.

Other examples include selecting lottery numbers, choosing pizza toppings, forming a team, picking exam questions from a list, or choosing a subset from a larger group.