N Choose K Calculator n=2, k= result

Find out how many different ways you can choose k items from a set of n items 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.

Calculation:

The number of elements (n) must not be less than the number of selected elements (k). If n < k, the calculation proceeds with the values of n and k swapped.

C_{k} (n) = (k n) = \frac{n !}{k ! ( n - k ) !} n = 2 k = 4 C_{2} (4) = (2 4) = \frac{4 !}{2 ! ( 4 - 2 ) !} = \frac{4 \cdot 3}{2 \cdot 1} = 6

The number of combinations: 6

A bit of theory - the foundation of combinatorics

Combinations

A combination of the 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 the order does not matter. In mathematics, such unordered groups are called sets and subsets. The count is called a combination number and is calculated as follows:

C_{k} (n) = (k n) = \frac{n !}{k ! ( n - k ) !}

A typical example: we have 15 students and need to choose 3. How many ways can this be done?

N Choose K Calculator n=2, k= result

Calculation:

The number of combinations: 6

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems