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Combination Calculator - nCr Formula

Free combination calculator. Calculate nCr - the number of ways to choose r items from n items where order doesn't matter.

Combination Calculator

Calculate nCr - unordered selections

Enter the total number of items.

Enter how many items to choose (r ≤ n).

Result

Enter your values to see results

and click the "Calculate" button

What is Combination?

A combination is a selection of items where ORDER DOESN'T MATTER. For example, choosing 3 people from 10 for a committee - the selection {A,B,C} is the same as {C,B,A}.

Combination Formula

C(n,r) = n! / (r! × (n-r)!)

Example: C(10,3) = 10!/(3!×7!) = 120 ways. Also written as "n choose r" or (n r)

Frequently Asked Questions

What is the difference between combination and permutation?
In combinations, order doesn't matter (ABC = CBA). In permutations, order matters (ABC ≠ CBA). Use combinations for teams, committees, and selections.
What is a binomial coefficient?
C(n,r) is also called a binomial coefficient because it appears in the binomial theorem expansion of (a+b)^n. It's often written as (n r) or "n choose r".

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