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Maths Exercices

Variations with repetition

Given a set A of n different elements and m a whole number, m (m<n). In how many ways can we choose m elements from A?

The answer depends on the exact conditions of choice:

When the ordering of objects matters, and an object can be chosen more than once, we are talking about variations with repetition, and the number of variations is:


where n is the number of objects from which you can choose and m is the number of objects we can choose (repetitions allowed)


How many words of 2 letters can you make with 4 letters a,b,c,d?.
The subsets are the following:

{aa} {ab} {ac} {ad}
{ba} {bb} {bc} {bd}
{ca} {cb} {cc} {cd}
{da} {db} {dc} {dd}
There are 16 total variations on the set.
Using the formula: VR4,2=42=16

Enter the number of elements of the set A and choose a number m (m<n). The computer will calculate you how many variations with repetition of m elements are there?

n = m =