Permutation Calculator
This permutation calculator is a tool that will help you determine the number of permutations in a set (often denoted as nPr). Read on to learn:
- The permutation definition;
- Permutation formula; and
- The relation between permutation and combination.
Permutation definition
A permutation is the number of ways in which you can choose r elements out of a set containing n distinct objects, where the order of the elements is important.
For example, imagine that you have a deck of nine cards with digits from 1 to 9. You draw three random cards and line them up on the table, creating a three-digit number. How many distinct numbers can you create?
Permutation formula
Luckily, you don't have to write down all of the possible numbers. You can use a formula that will allow you to calculate the number of permutations in no time:
where:
- PP is the number of permutations;
- nn is the total number of elements in the set; and
- rr is the number of elements you choose from this set.
The exclamation mark represents a factorial. Check out our factorial calculator for more information on this topic.
You may also notice that, according to the permutation formula, the number of permutations for choosing one element is simply nn. On the other hand, if you have to select all elements, the formula gets reduced to P(n,n)=n!P(n,n)=n!.
Let's apply this equation to our problem with numbered cards. We need to find the number of ways to choose 3 out of 9 cards:
You can check the result with our nPr calculator.
Permutation and combination
When you select a corresponding checkbox, you can find the number of combinations as well. Combinations are also ways to choose rr out of nn elements. Unlike in permutations, the order of the combinations doesn't matter.
For example, imagine a bag filled with twelve balls, each one of a different color. You pick five balls at random. How many distinct sets of balls can you get?
If you know the number of permutations, you can easily calculate the number of combinations, too:
You can also check out dedicated tool: permutation and combination calculator.
What next?
Make sure to try our probability calculator if you are interested in probability problems.
You can also try to solve a more difficult problem with our permutation calculator: if you have a deck of 9 cards with digits from 0 to 8, how many distinct valid numbers can you create by picking three cards at random? A number is not valid if it starts with zero.
FAQs
- What does the Permutation Calculator do?
- Use the permutation calculator to determine the number of permutations in a set. Use the calculator above for instant results in your browser.
- Is the Permutation Calculator free to use?
- Yes. All Try To Calculator tools are free and do not require an account.
- Are my inputs stored or sent to a server?
- No. Calculations run locally in your browser. We do not collect the numbers you enter or the results shown.
- Can I use the Permutation Calculator for professional decisions?
- This tool is for education and quick estimates. For medical, legal, tax, or financial decisions, verify results with a qualified professional.
- Where can I find related calculators?
- Browse more Statistics tools on Try To Calculator at /statistics, or use the related calculators section on this page.
Related calculators
5★ rating average
The rating average calculator returns an average rating based on the number of 1-5 ratings.
Statistics
Dice probability
With this dice probability calculator, you can easily find the various probabilities related to rolling a set of dice.
Statistics
Critical value
The critical value calculator helps you find the one- and two-tailed critical values for the most widespread statistical tests.
Statistics
Coin flip probability
Coin flip probability calculator lets you calculate the likelihood of obtaining a set number of heads when flipping a coin multiple times.
Statistics