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 \(\text{15}\).