Combinations calculator

The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination with 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 repeated).

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 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

Divisions 4044
School players scored seven goals in the match. List all possible goal divisions into three-thirds and add up how many.