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Our permutation calculator helps you to arrange elements from the set of elements in proper order. It arranges element in two different ways they are ordered without repeating (distinct) elements and with repeating elements.

The permutation is a process of arranging or rearranging a set of element in order. This process is called "permuting" and permutation denoted as nPr or P(r, n) or n P r.

It arranges "r" elements from a set of "n" element then permutation is

P (n, r) = n! / (n-r)!

Here one of the important things we need to understand that arrangement can possible with two different ways.

1.Repetition.

2.Without repetition.

If we want to understand this concept we need to look out an example.

Example:

Find the number ways 2 digit numbers can we make with digits 1, 2, 3, 4?

1.Digits cannot be repeated (distinct objects).

2.Digits can repeat.

Digits cannot be repeated:

Probability of the first position to be filled is 4 & probability of the second position filled is 3 then total permutation is 4 X 3 = 12.

By using for permutation formula we can calculate two-digit numbers formed by four digits.
P (n, r) = n! / (n-r)!

Where n = total number digits; r = arrange digits.

P (4, 2) = 4! / (4-2)!

P (4, 2) = 12.

So the number of ways we can arrange 2 digits numbers from 4 digits without repeated numbers is 12 they are

1, 2 2, 1 3, 1 4, 1

1, 3 2, 3 3, 2 4, 2

1, 4 2, 4 3, 4 4, 3

Digits can repeat:

In this case, we need to arrange 2 digit numbers by using 4 digits with condition digits can repeat.

Probability of first position to be occupied by a number is 4. Probability of the second position to be occupied by a number is 4. So the number of permutations possible is = 4 X 4 = 16 ways.

Here we determine the total number of ways to choose is

1, 1 2, 1 3, 1 4, 1

1, 2 2, 2 3, 2 4, 2

1, 3 2, 3 3, 3 4, 3

1, 4 2, 4 3, 4 4, 4

Our permutation calculator calculating permutations with repetition and without repetition. Follow the below steps to calculate permutations.

Step 1:

Open Permutation Calculator.

Step 2:

Enter n, r values.

Step 3:

Click on calculate.