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Calculate P(n,r) and C(n,r) with step-by-step formulas.
Permutation & Combination is a free browser-based tool that helps you calculate p(n,r) and c(n,r) with step-by-step formulas. It is part of ToolsMonk's student tools collection, so you can finish the job without downloading software, creating an account, or jumping between multiple websites.
This tool is especially useful for workflows such as solving permutation and combination problems, probability and statistics homework, and counting arrangements or selections. Because it runs directly in your browser, you can use it on desktop, tablet, or mobile while keeping the process fast and easy for one-off tasks as well as repeat work.
Permutation & Combination is designed for people who want a practical, privacy-friendly workflow with instant results inside the larger ToolsMonk library.
Enter n (total items) and r (number chosen)
The tool calculates both nPr (permutations) and nCr (combinations)
Read the result for your problem
Use the explanation to pick the right one
Calculates permutations (nPr) and combinations (nCr)
From n (total items) and r (chosen items)
Clear results for probability and statistics
Explains when to use each
Runs in your browser — nothing is uploaded
Free, with no signup
Solving permutation and combination problems
Probability and statistics homework
Counting arrangements or selections
Checking nPr / nCr values
Permutation & Combination is a powerful free online tool available on ToolsMonk that helps you calculate p(n,r) and c(n,r) with step-by-step formulas. Whether you're a professional, student, or casual user, our permutation & combination provides instant, accurate results right in your browser without requiring any software installation or account creation.
As part of our Student Tools collection, this tool is designed with simplicity and power in mind. All processing happens client-side, ensuring your data remains completely private and secure. The tool works seamlessly across all modern browsers on desktop, tablet, and mobile devices.
Permutation-Combination Calculator computes nPr (permutations) and nCr (combinations) from n total items and r chosen — the core counting tools of probability and statistics.
The whole distinction comes down to one question: does order matter? Permutations count arrangements where it does (a race podium, a password, a sequence), while combinations count selections where it doesn't (a committee, a hand of cards, a group). Asking 'if I rearrange the chosen items, is it a different outcome?' resolves almost every permutation-vs-combination problem.
Mathematically, nPr = n! ÷ (n−r)! and nCr = n! ÷ (r!(n−r)!) — the only difference being that combinations divide by an extra r! to strip out the duplicate orderings permutations count separately. That's why nCr is always less than or equal to nPr for the same inputs.
Because these use factorials, the numbers explode quickly (10! exceeds 3.6 million), which is exactly why they're calculated rather than counted by hand. The calculation runs in your browser with nothing uploaded. Pair it with the Logarithm and other ToolsMonk student and STEM tools for your maths coursework.
Ask 'does order matter?' — yes = permutation (nPr), no = combination (nCr)
nCr is always ≤ nPr because it ignores the duplicate orderings permutations count
Passwords/rankings = permutations; hands/groups/selections = combinations
Common questions about this tool, its workflow, and what to expect before you use it.
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