Variations Calculator - Permutations with Repetition

n (number of objects):

The number of different objects available

k (number of positions):

The length of each arrangement

Result

V(n,k)

About Variations (Permutations with Repetition)

Variations, also known as permutations with repetition, count the number of ways to arrange n different objects in k positions, where each object can be used multiple times.

Formula:

\[V(n,k) = n^k\]

For example:

With n=3 objects (say, A, B, C) and k=2 positions: V(3,2) = 3² = 9 arrangements
The arrangements are: AA, AB, AC, BA, BB, BC, CA, CB, CC

Applications include:

Password combinations (n characters available, k positions)
DNA sequence analysis (4 bases, multiple positions)
Musical compositions (n notes, k positions)
Computer algorithms and coding theory

Note: The result grows exponentially with k. For large values, the result might be a very large number.