About Our Permutation and Combination Calculator

Permutation and Combination are words closely associated, but they have a distinct meanings. These are part of Mathematics, known as Combinatorics. Permutation involves selecting elements within a set where the way of arrangement matters. Unlike Permutation, the Combination involves selecting elements from the set without a determined order.

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 elements, including discrete, finite numbers.

Note: The permutation and combination 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 set has 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 different formulas. The permutation calculator is specially designed to calculate the sets with no repetition.

The general formula to calculate Permutation with no repetition is:

(n - r)!

Where, 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 quickly and saves a lot of brainstorming.

What is Combination?

The Combination is a selection of a sample set from the collection of objects so that the order of selection does not matter.

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

Like the Permutation, the Combination calculator also considers the cases without replacements. Calculate the results with our ncr calculator in seconds and save time.

E.g. Among 5 equally 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 :

  1. Maggi, Joy, Matthew
  2. Maggi, Joy, Grace
  3. Maggi, Joy, Megan
  4. Maggi, Matthew, Grace
  5. Maggi, Matthew, Megan
  6. Maggi, Grace, Megan
  7. Joy, Matthew, Grace
  8. Joy, Matthew, Megan
  9. Joy, Grace, Megan
  10. Matthew, Grace, Megan

For calculation, the equation for the Combination

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

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

(There are 10 ways to arrange a 3-membered group from the given 5 students.)

Use of Permutation and Combination Calculator.

Combinations and permutations 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), quantum physics to describe Particles, and Biotechnology for decoding RNA sequences.


  • Permutation and combination calculator are minimal and operate quickly: It features advanced algorithms to measure and transform the result into a series, which can calculate large numbers quickly.
  • 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 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 simultaneously.
  • 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 a 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.” The solution will instantly appear on the screen as soon as you click.