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.

(n)
(k)

Calculation:

Ck​(n)=(kn​)=k!(n−k)!n!​  n=10 k=4  C4​(10)=(410​)=4!(10−4)!10!​=4⋅3⋅2⋅110⋅9⋅8⋅7​=210

The number of combinations: 210



A bit of theory - the foundation of combinatorics

Combinations

A combination of a k-th class of n elements is an unordered k-element group formed from a set of n elements. The elements are not repeated, and it does not matter the order of the group's elements. In mathematics, disordered groups are called sets and subsets. Their number is a combination number and is calculated as follows:

Ck​(n)=(kn​)=k!(n−k)!n!​

A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?

Foundation of combinatorics in word problems



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