n choose k calculator

Find out how many different ways you can choose k items from n items set without repetition and without order. This number is also called combination number or n choose k or binomial coefficient or simply combinations. See also general combinatorial calculator.

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Calculation:

C_k(n) = {n choose k} = fraction{ n! }{ k! (n-k)!} ; ; C_{{ 4}}(10) = {{ 10} choose 4} = fraction{ 10! }{ 4!(10-4)!} = fraction{ 10 * 9 * 8 * 7 } { 4 * 3 * 2 * 1 } = 210 ; ;

Number of combinations: 210