Combinations Calculator

The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination without repetition of k objects from n is a way of selecting k objects from a list of n. The order of selection does not matter and each object can be selected once (without repetition).

Calculation:

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?

Combinations Calculator

Calculation:

The number of combinations: 210

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems