Combinations & Permutations (nCr, nPr)

About this calculator

This calculator computes combinations (nCr), permutations (nPr) and the factorial (n!) from two inputs, n (the total number of items) and r (how many are being chosen or arranged). Permutations count arrangements where order matters, combinations count selections where order doesn't, and both formulas are built from the factorial function, which itself multiplies every whole number from 1 up to n.

These formulas are core to probability and statistics coursework, where students calculate the odds of a specific hand, drawing, or arrangement occurring out of all possible outcomes. Outside the classroom, the same math shows up whenever someone needs to know how many possible outcomes exist — the number of ways to arrange a race's finishing order, the number of possible lottery ticket combinations, or how many different teams of a given size can be formed from a larger group — situations that come up in game design, scheduling and odds calculation alike.