Factorial, Permutation & Combination Calculator

What is a factorial, permutation, and combination calculator?

This tool computes three counting operations: factorials (n!), permutations P(n, r) which count ordered arrangements, and combinations C(n, r) which count unordered selections. They’re the building blocks of probability and combinatorics.

How this calculator works

• Choose factorial, permutation, or combination and enter n (and r where needed).
• Factorial multiplies n by every positive integer below it — 5! = 120.
• Permutations = n! ÷ (n−r)!, combinations = n! ÷ (r! × (n−r)!).
• Very large results are shown in scientific notation so they stay readable.

How to use the result

1. Use combinations when order doesn’t matter — picking 3 winners from 10 is C(10,3).
2. Use permutations when order matters — arranging 3 of 10 people in a line is P(10,3).
3. Use factorial for arranging everything — seating 10 guests is 10!.
4. Check your problem statement: “how many ways to choose” vs. “how many ways to arrange” is the whole difference.

What’s the difference between permutations and combinations?

Permutations count arrangements where order matters — P(10,3) = 720, because ABC and CBA are different. Combinations count selections where order doesn’t — C(10,3) = 120, because ABC and CBA are the same three items. Divide by r! to go from permutations to combinations.

Common mistakes

• Using the wrong one. If order doesn’t matter, it’s a combination; permutations are bigger because they count every ordering.
• Allowing r > n. You can’t choose or arrange more items than exist — the calculator rejects it.
• Expecting exact decimal output for huge results. 170! has over 300 digits; scientific notation is the honest representation.

Counting problems pair naturally with probability and statistics — the standard deviation calculator and average median mode calculator handle the data side, and the random number generator demonstrates the outcomes being counted.