# Permutation Calculator

Welcome to the Permutation Calculator. This tool allows you to calculate the number of permutations for a given set of items. A permutation is the grouping of objects in a particular order. This is often used in probability and statistics.

** Result :**

## How to Use the Permutation Calculator

**Enter the Value of n (Total Number of Items)**Locate the input field labeled "Enter n value." Enter the total number of items or elements in this field. This is the number from which you are selecting items to arrange.

**Enter the Value of r (Number of Items to Arrange)**Locate the input field labeled "Enter r value." Enter the number of items you want to arrange from the total number of items.

**Calculate the Permutation**After entering the values for n and r, click the "Calculate" button. The calculator will process the input and display the result, showing the number of permutations possible.

**Review the Detailed Solution**The calculator will provide a step-by-step solution using the permutation formula \( \mathrm{ \mbox{nPr} = \frac{n!}{ (n-r)!} } \). Review the detailed steps to understand how the result was computed.

## Permutation Formula

The permutation formula is used to determine the number of possible arrangements in a set when the order of the elements matters. The formula is given by:

\( \mathrm{ \mbox{nPr} = \frac{n!}{ (n-r)!} } \)

Where:

**n**= Total number of items**r**= Number of items to arrange

This formula calculates the number of ways to arrange **r** items out of a total of **n** items.

## npr calculator

Use our permutation calculator to calculate permutation of give number below is the example of permutation.

### calculator p(15,4) with npr

Given : \(\mathrm{ n = 15}\), \(\mathrm{r = 4}\)

The number of ways to select \(4\) numbers out of \(15\), regard to order, can be calculated using the permutation formula, which is

\( \mathrm{ \mbox{nPr} = \frac{n!}{ (n-r)!} } \)

In this case, we want to select \(4\) items from a pool of \(15\), and the order in which we select them matters. Therefore, we use the formula:

\( \begin{align} \mathrm{\mbox{nPr}} &= \mathrm{ \frac{n!}{(n-r)!}} \\ &=\mathrm{ \frac{\text{15}!}{ (\text{15}-\text{4})!}} \\ &= \mathrm{ \frac{\text{15}!}{ \text{11}!}} \\ &=\text{32,760} \end{align} \)

Therefore, there are \(\text{32,760}\) different permutations of \(\text{4}\) items that can be selected from a pool of \(\text{15}\).