n choose k calculator n=255, k=4 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 = 255 k = 4 C_{4} (255) = (4 2 5 5) = \frac{2 5 5 !}{4 ! ( 2 5 5 - 4 ) !} = \frac{2 5 5 \cdot 2 5 4 \cdot 2 5 3 \cdot 2 5 2}{4 \cdot 3 \cdot 2 \cdot 1} = 172061505

The number of combinations: 172061505

172061505

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?

n choose k calculator n=255, k=4 result

Calculation:

The number of combinations: 172061505

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems