## Definition of Permutation

Basically Permutation is an arrangement of objects in a particular way or order. While dealing with permutation one should concern about the selection as well as arrangement. In Short, ordering is very much essential in permutations. In other words, the permutation is considered as an ordered combination.

## Representation of Permutation

We can represent permutation in many ways, such as:

## Formula

The formula for permutation of n objects for r selection of objects is given by:**P(n,r) = n!/(n-r)!**

For example, the number of ways 3rd and 4th position can be awarded to 10 members is given by:

P(10, 2) = 10!/(10-2)! = 10!/8! = (10.9.8!)/8! = 10 x 9 = 90

Click here to understand the method of calculation of factorial.

## Types of Permutation

**Permutation can be classified in three different categories:**

- Permutation of n different objects (when repetition is not allowed)
- Repetition, where repetition is allowed
- Permutation when the objects are not distinct (Permutation of multi sets)

Let us understand all the cases of permutation in details.

### Permutation of n different objects

If n is a positive integer and r is a whole number, such that r < n, then P(n, r) represents the number of all possible arrangements or permutations of n distinct objects taken r at a time. In the case of permutation without repetition, the number of available choices will be reduced each time. It can also be represented as: