Combination and Binomial Coefficient Calculator (nCr)
Counts selections where order does not matter, such as a hand of cards or a lottery draw.
Combinations
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Digits —
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The formula
nCr = C(n, r) = n! ÷ (r!(n − r)!) with repeats: C(n + r − 1, r)
Results below 10²¹ are exact. Larger ones go through logarithms and log-gamma, and are shown in scientific notation.
What to watch out for
The same value appears as the coefficient in the expansion of (a + b)ⁿ, which is why it is also called the binomial coefficient.
Frequently Asked Questions
How many 5-card hands are there?
2,598,960.
What is 10 choose 3?
120. That is the 720 ordered arrangements divided by the 6 orders of each selection.
How big is 1,000 choose 500?
About 2.7029×10^299.