# Permutation Calculator

Permutation Calculator calculates the number of possible ways of choosing r elements from a total of n elements when the order of arrangement matters. Permutations is a counting technique that is employed in various real-life situations.

## What is Permutation Calculator?

Permutation Calculator is an online tool that assists in calculating the number of possible permutations when r objects are selected from a total of n objects. In permutations the order in which the objects are arranged matters. To use this * permutation calculator*, enter the values in the input boxes.

### Permutation Calculator

*Use up to 5 digits only.

## How to Use Permutation Calculator?

Please follow the steps below to find the number of permutations using the online permutation calculator:

**Step 1:**Go to Cuemath’s online permutation calculator**Step 2:**Enter the total number of objects (n), and the sample size (r) in the given input boxes of the permutation calculator.**Step 3:**Click on the**"Calculate"**button to find the number of permutations.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Permutation Calculator Work?

Permutations and Combinations are principles of counting and are used to determine the different number of outcomes in a given situation. When we want to arrange objects in a definite order we use permutations. In contrast, combinations are used to find the number of possible groups when the order of arrangement does not matter. Permutations can be used for different kinds of things while combinations are used for things of the same type. Suppose we have to pick a first, second, and third place winner we will use the concept of permutations. However, if we have to pick three winners, combinations will be used. Permutations are widely used in the computer science industry to create various sorting algorithms.

To determine the number of permutations the following formula is used:

P(n,r) = n! / (n-r)!

Here n is the total number of objects and r is the number of objects that have to be chosen.

This formula implies that we are determining the number of possible permutations of selecting r objects from n distinct objects.

## Solved Examples on Permutations

**Example 1:** Find the number of ways in which the top 3 players can be ranked from a pool of 6 players and verify it using the permutation calculator.

**Solution:**

Total number of players (n) = 6

Required subset size (r) = 3

Number of possible permutations = P(n,r) = n!/(n-r)!

P(6,3) = 6!/(6-3)!

P(6,3) = 6!/(3)!

P(6,3) = 120.

Therefore, the total number of ways to rank the top 3 players from a pool of 6 players is 120.

**Example 2:** Find the number of 2 letter words that can be formed using the letters in the word SPICE and verify it using the permutation calculator.

**Solution:**

Total number of letters (n) = 5

Required subset size (r)= 2

Number of possible permutations = P(n,r) = n!/(n-r)!

P(5,2) = 5!/(5-2)!

P(5,2) = 5!/(3)!

P(6,3) = 20.

Therefore, the total number of 2 letter words that can be formed from the word SPICE is 20.

Similarly, you can try the permutation calculator to find the number of permutations for the following:

- How many distinct words can be formed using the letters of the word SQUARE?
- How many ways can 20 students be arranged in a row if 2 students, Kim and Cat, are not supposed to stand together?

**☛ Math Calculators:**

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