Combinations Calculator (nCr)

Find the Combinations:
C(n,r) where:
n =
r =

C(1,1) = 1! / 1! (1 - 1)! =
1

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Calculate the combinations for C(n,r) = n! / r! (n - r)!. For 0 <= r <= n.

Combinations Formula:

C(n,r) = n! / r! (n - r)!

The number of ways a sample of r elements can be obtained from n distinguishable objects where order does not count and repetitions are not allowed. [1] "The number of ways of picking r unordered outcomes from n possibilities." [2]

Also referred to as r-combination or "n choose r". In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k".

References

[1] Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 206, 2003.

For more information on combinations and binomial coefficients please see http://mathworld.wolfram.com/Combination.html