🎲Combination Calculator

Calculate the number of combinations C(n,r) for unordered selections.

n (pool size)

r (items to choose)

C(10,3) = 10! / (3! × 7!)

120

Ways to choose 3 items from 10 (order does not matter)

About Combination Calculator

Calculate the binomial coefficient C(n, r) — the number of ways to choose r items from n items where order does not matter. Also written as 'n choose r' or nCr. Enter n and r to get the result with the full factorial formula expanded step by step.

How to Use Combination Calculator

1
Enter n and r
Input the total pool size (n) and the number of items to select (r).
2
Calculate
Click Calculate to get C(n, r) with the formula and step-by-step calculation.
3
Use the result
Apply the combination count to lottery odds, probability, or selection problems.

Common Use Cases

Calculating lottery odds and prize probabilities
Counting ways to select a team or committee
Solving statistics and probability homework
Analysing possible poker hand combinations

Frequently Asked Questions

What is a combination?

A combination C(n, r) = n! / (r! × (n-r)!) counts selections where order is irrelevant — e.g. choosing 3 students from a class of 30. The group {A,B,C} is the same as {B,A,C}.

Can I calculate large values of n?

Yes — the calculator handles large factorials using an optimised algorithm to avoid overflow, supporting values of n up to several thousand.