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:

Ck(n)=(nk)=n!k!(nk)!  n=10 k=4  C4(10)=(104)=10!4!(104)!=109874321=210C_k(n) = \dbinom{ n}{ k} = \dfrac{ n! }{ k! (n-k)!} \ \\ \ \\ n = 10 \ \\ k = 4 \ \\ \ \\ C_{{ 4}}(10) = \dbinom{ 10}{ 4} = \dfrac{ 10! }{ 4!(10-4)!} = \dfrac{ 10 \cdot 9 \cdot 8 \cdot 7 } { 4 \cdot 3 \cdot 2 \cdot 1 } = 210

Number of combinations: 210