Combination & Permutation
Calculate nCr and nPr for counting problems. Free combinatorics calculator.
Results
nPr (permutations)
nCr (combinations)
Educational estimates · not financial advice · free, no signup
Formula / how it works
nPr = n!/(n−r)!. nCr = n!/(r!(n−r)!). Require 0 ≤ r ≤ n for standard definitions. Statistical outputs use classical definitions (mean, variance, combinations/permutations, binomial probabilities). Sample vs population variance is labeled when both exist. These are descriptive/educational helpers, not full hypothesis-test suites. For the Combination & Permutation, the labeled fields (n, r) drive the live result panel.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Counting problems ask whether order matters. MyCalcsWorld’s Combination & Permutation Calculator evaluates nPr and nCr so students can check contest and homework counting without expanding huge factorials by hand. Pair with Factorial tools for intermediate steps. Educational discrete math — watch overflow on large n. MyCalcsWorld keeps inputs labeled and formula notes visible so you can mirror the same scenario on paper when you need an audit trail. Core results run in the browser with no signup required for the calculator itself.
When to use / who it helps
- Homework nCr/nPr checks.
- Lottery-style combination counts.
- Password-style permutations (educational).
- Teaching order matters vs not.
- Comparing nPr vs nCr on the same n,r.
How to use
Steps
- Enter n.
- Enter r.
- Read permutations and combinations.
- State whether order matters in the word problem.
- Use Factorial for partial checks.
- Keep n modest for readable integers.
How to interpret results
- nCr ≤ nPr for the same n,r (r≥1).
- nC0 = 1.
- Educational counting.
- Display limits on large factorials.
- Not a probability engine by itself.
Common mistakes & gotchas
- Using combinations when order matters.
- r > n.
- Canceling factorials incorrectly by hand.
- Huge n overflowing display.
- Confusing with probability (need equally likely model).
Worked example
Worked example — n=10, r=3
- nPr = 10×9×8 = 720.
- nCr = 720/6 = 120.
- Choose 3 of 10 without order → 120.
- Ordered triples → 720.
Result: For n=10, r=3: 720 permutations and 120 combinations — order vs unordered selection side by side.
Want these demo numbers in the form? Tap Try example above the Calculate button.
How to calculate / formula
nPr = n!/(n−r)!. nCr = n!/(r!(n−r)!). Require 0 ≤ r ≤ n for standard definitions. Statistical outputs use classical definitions (mean, variance, combinations/permutations, binomial probabilities). Sample vs population variance is labeled when both exist. These are descriptive/educational helpers, not full hypothesis-test suites. For the Combination & Permutation, the labeled fields (n, r) drive the live result panel.
Frequently asked questions
Order matters?
Use permutations; otherwise combinations.
With replacement?
Different formulas — not this page’s default.
r > n?
Standard nCr/nPr undefined — fix inputs.
Probability?
Divide favorable by total only with a clear model.
Large n?
Use log-gamma style tools offline for huge values.
What does the Combination & Permutation on MyCalcsWorld actually compute?
Compute nCr and nPr for counting problems. You enter n, r, and the result panel updates in your browser — free, no signup. Below the form you will find when-to-use tips, common mistakes, a worked example, formula notes, and FAQs for this tool.
How do I use the Combination & Permutation step by step?
Start from the defaults (n 10, r 3) or type your own values into n, r. Watch the live results (and any chart or table). Then scroll to interpretation tips and the worked example before you rely on the figure for a real decision. Related Statistics tools sit in the sidebar and “You might also like” section.
Who is the Combination & Permutation for?
It helps students and analysts validating means, spreads, combinations, and classical probabilities on small datasets. If your case needs a neighboring metric, jump to a related tool rather than forcing the wrong inputs into this form.
Questions about this tool? Contact MyCalcsWorld · mycalcsworldcontact