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.

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


Result :


How to Use the Permutation Calculator

  1. 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.

  2. 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.

  3. 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.

  4. 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:

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 \(\text{15}\).