Combinations & Permutations Calculator
Calculate combinations (nCr), permutations (nPr), and factorials with step-by-step solutions. Perfect for probability, statistics, and combinatorics problems. Handles large numbers with BigInt precision.
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How to Use
- 1 Select calculation type — Choose between Combinations (nCr), Permutations (nPr), or Factorial (n!).
- 2 Enter n (total items) — Enter the total number of items in your set.
- 3 Enter r (items to choose) — For combinations and permutations, enter how many items to select (not needed for factorial).
- 4 Click Calculate — Press the Calculate button to compute the result.
- 5 Review the solution — View the result with formula, step-by-step breakdown, and real-world example.
💡 Pro Tip: Remember: use Combinations when order doesn't matter (choosing team members) and Permutations when order matters (ranking contestants).
Frequently Asked Questions
What is the difference between combinations and permutations?
Combinations (nCr) count selections where ORDER DOES NOT MATTER - like choosing 5 cards from a deck. Permutations (nPr) count arrangements where ORDER MATTERS - like assigning 1st, 2nd, 3rd place medals. For the same n and r, permutations always gives a larger result.
What is the formula for combinations (nCr)?
The combination formula is C(n,r) = n! / (r! × (n-r)!). For example, C(52,5) = 52! / (5! × 47!) = 2,598,960. This calculates how many ways to choose r items from n items when order does not matter.
What is the formula for permutations (nPr)?
The permutation formula is P(n,r) = n! / (n-r)!. For example, P(10,3) = 10! / 7! = 720. This calculates how many ways to arrange r items from n items when order matters.
What is a factorial?
A factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1. Factorials grow extremely fast - 20! is over 2 quintillion.
Can this calculator handle large numbers?
Yes! The calculator uses BigInt for precise calculations with arbitrarily large numbers. It can calculate factorials like 100! (which has 158 digits) and combinations like C(100,50) without losing precision.