Variations without repetition

The calculator computes the number of variations of the k-th class from n elements. Variation is a way of selecting k items from a collection of n items (k ≤ n), such that (like permutations) the order of selection does matter. The repetition of items is not allowed.

Calculation:

V_{k} (n) = \frac{n !}{( n - k ) !} n = 10 k = 4 V_{4} (10) = \frac{1 0 !}{( 1 0 - 4 ) !} = \frac{1 0 !}{6 !} = 10 \cdot 9 \cdot 8 \cdot 7 = 5040

The number of variations: 5040

A bit of theory - the foundation of combinatorics

Variations

A variation of the k-th class of n elements is an ordered k-element group formed from a set of n elements. The elements are not repeated, and the order of the group's elements matters.

The number of variations can be easily calculated using the combinatorial rule of product. For example, if we have a set of n = 5 numbers {1, 2, 3, 4, 5} and we need to make third-class variations, then V(3,5) = 5 × 4 × 3 = 60.

V_{k} (n) = n (n - 1) (n - 2) . . . (n - k + 1) = \frac{n !}{( n - k ) !}

n! is called the factorial of n, which is the product of the first n natural numbers. The factorial notation is clearer and equivalent. For calculations, it is sufficient to use the procedure derived from the combinatorial rule of product.

Variations without repetition

Calculation:

The number of variations: 5040

A bit of theory - the foundation of combinatorics

Variations

Foundation of combinatorics in word problems