Combination Calculator

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Calculate the number of ways to choose k items from a set of n distinct items, where order does not matter.

Selection Parameters

Total Items (n)

Items to Choose (k)

Combinations

C(52, 5)2,598,960

About this calculator

Combinations

A combination is a selection of items from a larger set where the order of selection does not matter. This is in contrast to permutations, where order is significant. Combinations answer questions like 'How many different 5-card hands can be dealt from a 52-card deck?'

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Pro Tips

n must be greater than or equal to k. If k > n, the answer is 0.
C(n, k) is the same as C(n, n-k). Choosing k items to keep is the same as choosing n-k items to discard.
The values of C(n, k) correspond to the entries in Pascal's Triangle.

Fun Facts

"The number of ways to pick lottery numbers is a classic combination problem."
"Binomial coefficients appear in the expansion of (x+y)^n."
"Combinatorics is a major field in mathematics and computer science."

Formula: C(n, k) = n! / (k!(n-k)!)