N Choose K Calculator n=10, 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 = 10 k = 4 C_{4} (10) = (4 1 0) = \frac{1 0 !}{4 ! ( 1 0 - 4 ) !} = \frac{1 0 \cdot 9 \cdot 8 \cdot 7}{4 \cdot 3 \cdot 2 \cdot 1} = 210

The number of combinations: 210

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=10, k= result

Calculation:

The number of combinations: 210

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems