## Permutation and Combination Calculator

To further understand, let us see an example, the set of numbers in a winning lottery ticket -34521. Any combination of these same numbers like 35142, 12453, or 12345 will not be eligible for the prize money. The order matters. Second Example, Set of fruits at the table – Orange, Apple, banana, kiwi, and Grapes. Here, the order doesn’t matter.

Permutation formula calculator can be used for a wide range of sets of elements including discrete, finite numbers.

Note: The calculator is designed for cases with no repetition. For instance, the combination lock with passcode 6-6-6 cannot be calculated.

### What is Permutation?

The definition of Permutation is partly or a whole arrangement of a collection of objects (set). There are two types of Permutation:

• Permutation with repetition
• Permutation without repetition

It simply means that some are set having the same elements multiple times like (1-1-6-2-9-2) and no identical elements in a set (1-5-9-8-6-4). Both types are calculated with a different formula. The permutation formula calculator used here is specially designed to calculate the sets with no repetition.

The general formula to calculate Permutation with no repetition is:

nPr
 n! (n - r)!

n = number of objects in a set

r = subset of n or sample set

E.g. From a set of numbers (1,2,3,4,5,6,7) how many 3-digit numbers can be formed without repetition?

Answer: There are 7 distinct numbers of which 3 are chosen at a time.

nPr = 7!

(7 - 3)!

Therefore, n = 7 and r = 3

=7! / 4! = (7)(6)(5) = 210

The permutation formula calculator can easily calculate the results within no time at all and saves a lot of brainstorming.

### What is Combination?

The combination is a selection of sample set from the collection of objects, in such a way that the order of selection does not matter.

It is generally denoted as nCr, nCr, C(n,r), or (n/r).

Like the Permutation, Combination formula calculator also considers the cases without any replacements.

E.g. Among 5 equal capable students (Maggi, Joy, Matthew, Grace, Megan) 3 students are to be selected for a plantation project.

They can be assorted in the following ways :

• Maggi, Joy, Matthew
• Maggi, Joy, Grace
• Maggi, Joy, Megan
• Maggi, Matthew, Grace
• Maggi, Matthew, Megan
• Maggi, Grace, Megan
• Joy, Matthew, Grace
• Joy, Matthew, Megan
• Joy, Grace, Megan
• Matthew, Grace, Megan

For calculation the equation for the combination

nCr
 n! !r x (n - r)!
nCr
 5! !3 x (5 - 3)!

= 5! / 3! * 2! = (5) (2) = 10

(There is a total of 10 ways to arrange a 3 membered group from the given 5 students.)

#### Use of Permutation and Combination Calculator

Combination and permutation calculator can be used in different fields. It has a distinct significance in real life. It is used almost in every branch of mathematics, computer science (for analyzing and sorting the algorithms), In quantum physics to describe Particles, and in Biotechnology for decoding RNA sequence.

#### Functions

• permutation and combination calculator are minimal and operates quickly: It features advanced algorithms to measure and transform the result into a series, which can calculate large numbers in a very short time.
• Displays the number of the results in scientific notation format (exponential form) or entirely displays the digits. For Configurations, you can modify the minimum format number. The outcome that is lower than this minimum would be entirely represented in digits.
• Instant run: as you fill in 2 fields (n and r), the results will appear as you type at the same time.
• Combination and permutation calculator are capable of copying output.
• Good and modern interface.
• Simple and quick to use.

#### How to use permutation and combination calculator

The use of permutation and combination calculator is extremely easy. The calculation requires the entry of n (number of a set) and r (sample set number). After entering the given n and r of the problem click on “Calculate”. As soon as you click the solution will instantly appear on the screen.