n choose k calculator n=20, k=12 result

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.

Calculation:

C_{k} (n) = (k n) = \frac{n !}{k ! ( n - k ) !} n = 20 k = 12 C_{12} (20) = (1 2 2 0) = \frac{2 0 !}{1 2 ! ( 2 0 - 1 2 ) !} = \frac{2 0 \cdot 1 9 \cdot 1 8 \cdot 1 7 \cdot 1 6 \cdot 1 5 \cdot 1 4 \cdot 1 3}{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 125970

The number of combinations: 125970

125970

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:

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

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

Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers?