N Choose K Calculator n=20, k=5 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:

C_{k} (n) = (k n) = \frac{n !}{k ! ( n - k ) !} n = 20 k = 5 C_{5} (20) = (5 2 0) = \frac{2 0 !}{5 ! ( 2 0 - 5 ) !} = \frac{2 0 \cdot 1 9 \cdot 1 8 \cdot 1 7 \cdot 1 6}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 15504

The number of combinations: 15504

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=20, k=5 result

Calculation:

The number of combinations: 15504

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems