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Maths Exercices

Variations without repetition

Take a set A of n different elements. Choose m elements in a specific order.
Each such choice is called a variation of n elements choose m. How many variations are there?

The number of variations is given by the formula:
Vn,m=n(n-1)(n-2).....(n-m+1),
or what is equivalent:


Let's see the following example:

If we have a set {0, 1, 2, 3}, then the variations of size 2 are all the permutations of subsets of size 2. The subsets are the following:

{0, 1} {0, 2} {0, 3} {1, 2} {1, 3} {2, 3}
{1, 0} {2, 0} {3, 0} {2, 1} {3, 1} {3, 2}

There are 12 total variations on the set.

Using the formula:

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

n = m =
Vn,m=