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Enter n up to 1000 and an optional r to get n!, nPr and nCr as full BigInt integers, with the expansion formula shown.

📘 How to Use

  1. Enter the number (n) you want to calculate.
  2. Enter the number to choose (r) if needed (for permutation/combination calculations).
  3. View the calculation results for factorial, permutation, and combination.

Factorial, Permutation and Combination Calculator

Compute n!, nPr and nCr up to n=1000 with full BigInt integers

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Calculate Factorials, Permutations, and Combinations | Solve n!, nPr, and nCr

Instantly calculate factorials or determine the number of ways to arrange and select items. From probability homework to algorithm analysis, this tool processes massive numbers with infinite precision.

💡 How It Works

This tool computes the three pillars of combinatorics using BigInt logic, ensuring accuracy for massive results that would break standard calculators.

  • Factorial (n!): Multiply all positive integers up to n.
  • Permutation (nPr): Calculate the number of ways to order r elements from a set of n.
  • Combination (nCr): Calculate the number of ways to select r elements from a set of n where order doesn't matter.

📘 Pro Tips

  • Get All Results at Once: Simply enter 'n' (total) and 'r' (selected) to see the factorial, permutation, and combination results simultaneously.
  • Solve Massive Numbers: Go beyond the 16-digit limit of standard calculators. We support calculations like 1,000! with full precision.
  • Visualize the Logic: View the formula expansion (e.g., 5 × 4 × 3...) to verify your steps or help with your studies.

🧐 FAQ

How large can the numbers go? Most modern browsers handle up to 1000! or higher with ease. Note that the output string for these values will be exceptionally long.

Why are negative numbers blocked? In standard combinatorics, factorials are defined for non-negative integers. Negative values require the Gamma function, which falls outside the scope of discrete mathematics.

When should I use nPr vs. nCr? Use nPr (Permutation) when the sequence matters (like a PIN code or race results). Use nCr (Combination) when you only need to choose a group (like selecting a committee or drawing lottery numbers).

📚 Trivia

Did you know that 52! (the number of ways to shuffle a standard deck of cards) is so large that every time you shuffle a deck thoroughly, you are likely holding a sequence of cards that has never existed before in the history of the universe? It is roughly $8 \times 10^{67}$, which easily dwarfs the number of atoms on Earth.