P(n,r)
C(n,r)

Permutation & Combination Calculator at our Percentage Calculator Hub

Stuck on a probability problem at 11pm the night before your exam? You're in the right place. This tool lives in the same toolbox as our popular percentage calculator, so if you've already used that for quick homework checks, you know the drill: type your numbers, get your answer, move on with your life. Permutations and combinations trip up almost everyone the first time around because the formulas look almost identical but mean very different things. P(n,r) cares about the order things are arranged in, while C(n,r) just cares about which items end up in the group. Instead of mixing up factorials on scratch paper, you can punch in your

How to use Permutation & Combination Calculator at our Percentage Calculator Hub

  1. Enter n. Type the total number of items you're choosing from. This is the bigger number in P(n,r) and C(n,r).
  2. Enter r. Type how many items you want to pick or arrange. Just make sure r is less than or equal to n, otherwise the math breaks.
  3. Hit calculate. Click the button and the tool spits out both the permutation and combination values in one shot — no need to run two separate calculators.
  4. Compare the results. Permutations will always be bigger or equal to combinations because order matters. Use this as a sanity check before writing your answer down.
  5. Pick the one your question wants. If the problem says 'arrange', 'order', or 'line up', use P(n,r). If it says 'choose', 'select', or 'group', use C(n,r).
  6. Show your work. Copy the formula expansion into your homework so your teacher sees you understood the steps, not just the final number.

Frequently asked

What's the actual difference between permutation and combination? Permutation cares about order (ABC and CBA count as different). Combination doesn't (ABC and CBA are the same group). That's literally the whole game.
Why is P(n,r) always bigger than C(n,r)? Because every combination can be rearranged in r! different orders, and each of those rearrangements counts as its own permutation. So P(n,r) = C(n,r) × r!.
Can r ever equal n? Yep. P(n,n) equals n! (all the ways to arrange every item), and C(n,n) equals 1 (there's only one way to pick everyone).
What if r is bigger than n? It's not possible without repetition — you can't choose 7 things from a pool of 5. The calculator will flag that as invalid input.
Does this work for big numbers like 50 or 100? Yes, but factorials grow ridiculously fast. The output might use scientific notation once the values get huge, which is normal for high n values.
How do I know which formula my homework wants? Look for keywords. 'Arrange', 'order', 'rank', 'line up' point to permutation. 'Choose', 'select', 'pick', 'team', 'committee' point to combination.
What other math tools do you offer for studying? Tons. Beyond the percentage calculator, we've got a fraction calculator for converting messy decimals, an area calculator for geometry, a volume calculator for 3D shapes, and a standard deviation calculator for stats class.
More in this category

Tools you might also like

Area Calculator + Quick Percentage Calculator Crunch area and perimeter for any shape in seconds, then jump to our percentage calculator for grades. Free, fast, and made for late-night homework. Exponent Calculator (Plus a Percentage Calculator When You Need It) Free exponent calculator that solves a^b for any real numbers. Get instant answers, clear steps, and a built-in percentage calculator for homework. Factorial Calculator & Percentage Calculator Companion Compute factorials from 0! to 170! in seconds. A handy study tool for combinations, probability, and our percentage calculator companion. Percentage Calculator + Fraction Helper Free percentage calculator and fraction tool for students. Add, subtract, multiply, and divide fractions in seconds, with clear step-by-step results. GCD & LCM Calculator (Plus a Handy Percentage Calculator Companion) Find the GCD and LCM of any numbers in seconds. Free online tool for students — pairs nicely with our percentage calculator for quick math homework. Logarithm Calculator: Solve log_b(x) for Any Base Crack any logarithm in seconds. Solve log_b(x) for any base with steps. A handy percentage calculator companion for homework, exams, and study sessions. Mean, Median, Mode (and Percentage Calculator) in One Click Find mean, median, mode, and range fast. A free percentage calculator for stats homework — paste your numbers, get clean answers and steps. Percentage Calculator for Homework, Grades & Quick Math Free percentage calculator: find percent of a value, percent change, increase or decrease in seconds. Perfect for homework, test prep, and grade math. Prime Factorization Made Simple at Our Percentage Calculator Hub Break any integer into its prime factors instantly. Free, fast, and built for homework help — paste a number, hit go, and see the full factor tree. Quadratic Equation Solver — pairs nicely with our percentage calculator Solve ax² + bx + c = 0 in seconds. Get real or complex roots plus the discriminant — free, fast, and built to make homework less painful. Ratio Calculator with Built-In Percentage Calculator Simplify any a:b ratio in seconds with our free ratio and percentage calculator. Perfect for homework, lab reports, and quick study checks. Square Root & Cube Root Solver (with Percentage Calculator) Find √x and ∛x in one click. A fast square and cube root tool paired with a handy percentage calculator built for homework, exams, and quick checks.

Have an idea for a tool?

Tell us what you’d like to see — we ship the most-requested tools every week.