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Combinations Calculator

🎲 Statistics & probability. Use the Combinations (n choose r) formula to find combinations, n, r: pick the value you want, type the others, and the answer updates as you go.

nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n - r)!}
Combinations120

Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.

What each letter means

QuantityUnit
Combinationsno unit
nno unit
rno unit

Worked example

Find the combinations when n = 10, r = 3.

Using ⁿCr = n!/(r! (n - r)!): Combinations = 120.

Frequently asked questions

What is the formula for Combinations (n choose r)?

ⁿCr = n!/(r! (n - r)!).

What do the letters stand for, and what units are used?

Combinations, n, r.

How do you calculate combinations?

Put the values into ⁿCr = n!/(r! (n - r)!). For example, with n = 10, r = 3, combinations = 120.

Can I solve for a different value?

Yes. In the calculator above, pick the circle next to any value (combinations, n, r) and fill in the others: it rearranges the formula for you.

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