# Permutation Example Problems

Given below permutation example problems with solution for your reference. Permutation is the process of rearranging all the elements of a set in a sequential order. It also involves rearranging the ordered elements. It is otherwise called as arrangement number or order. Provided below permutation problems with solution to make you clearly understand the possible ways of arrangements of elements given.

## Permutation Problems with Solutions

###### Example 1:

Let us consider the problem: If three alphabets are to be chosen from A, B, C, D and E such that repetition is not allowed then in how many ways it can be done?

###### Solution:

We can calculate Permutation using the given formula.

#### Formula:

_{n}P_{r} = n! / ( n - r )!
**Substituting the values in the above given formula,**
Permutation: _{5}P_{3} = 5! / ( 5 - 3 )!
= (5 x 4 x 3 x 2 x 1) / 2 !
= (5 x 4 x 3 x 2 x 1) / 1 x 2
= 5×4/ 1 x 2
= 20/2
=10
**Hence, there are 10 possible ways.**

###### Example 2:

Refer the below permutation problem with solution. 10 students have appeared in a test in which the top three will get a prize. How many possible ways are there to get the prize winners?

###### Solution:

**Substituting the values in the above given formula,**

Permutation: _{10}P_{3} = 10! / ( 10 - 3 )!
= 10! / 7 !
= (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
= 10 x 9 x 8
= 720

Therefore, the value of **Permutation is 720**.

Permutations occur in every area of mathematics. It is the ordered combination of the elements. In group theory, permutation of set 'S' which is defined as bijection from 'S' to itself. In this function, every element occurs exactly one time as a value. Given permutation example problems with solution helps to find the possible way arrangements of the ordered data set.