# Permutation and Combination Example Problems

Permutation is a process of rearrangement of objects sequentially and it is an ordered combination whereas combination is the selection of objects without considering the order. Given below permutation and combination example problems with solutions for reference.

## Permutation and Combination Sample Problems with Solutions

###### Example 1:

Let us consider the sample problem: How many 7 digit land-line numbers can be formed if each number starts with 2 and 6 but no digit appears more than once.

###### Solution:

We can calculate different permutations using the given formula.

#### Formula:

Permutation nPr = n! / ( n - r )!
Combination nCr = nPr / r!

Note :

No digit appears more than once and hence we have 8 digits remaining (0,1,3,4,5,7,8,9)

Here, the next 5 places can be filled with the remaining 8 digits in 8P5 ways.

Permutation: nPr = 8! / ( 8 - 5 )! = 8! / 3! = (8 x 7x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 8 x 7x 6 x 5 x 4 = 6720 Therefore, the value of Permutation is 6720 .

###### Example 2:

Refer the below Permutation and Combination practice problem with solution. In a school, how many ways the school pupil leader, assistant school pupil leader and a class leader is selected from among 10 students?

###### Solution:

Substituting the values in the above given formula,

Permutation: nPr = 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 Combination: nCr = 720 / 3! = 720 / (3 x 2 x 1) = 120

Therefore, the value of Permutation is 720 and Combination is 120 .