What formulas does this calculator use?

Without repetition: permutations nPr = n!/(n−r)!, combinations nCr = n!/[r!(n−r)!]. With repetition: permutations = n^r, combinations = C(n+r−1, r).

What are valid inputs?

n and r must be non-negative integers. If repetition is not allowed, r ≤ n. With repetition allowed, r can exceed n.

How are large results handled?

Exact results are computed using BigInt (integer arithmetic). A scientific-notation approximation is also shown using logarithms.

Yes. Everything runs completely in your browser; nothing is uploaded or stored.

Permutation & Combination Calculator (nPr, nCr, with/without repetition)

Permutation & Combination Calculator (nPr, nCr)

Enter n (total distinct items) and r (items chosen). Select if order matters and if repetition is allowed.

n (total items) Non-negative integer

r (items chosen) Non-negative integer

Order Order matters (Permutation)
Order doesn’t matter (Combination)

Repetition Without repetition
With repetition allowed

Results will appear here.

Formulas Used

Let \(n\) be the number of distinct items and \(r\) the number chosen.

Permutations, no repetition: \( \displaystyle P(n,r) = \frac{n!}{(n-r)!} \)
Combinations, no repetition: \( \displaystyle C(n,r) = \binom{n}{r} = \frac{n!}{r!(n-r)!} \)
Permutations with repetition: \( \displaystyle n^r \)
Combinations with repetition: \( \displaystyle \binom{n+r-1}{r} \)

Exact values are computed with BigInt. A scientific-notation approximation is also provided.

Frequently Asked Questions

When should I pick permutations vs combinations?

Pick permutations when order matters (e.g., passwords, race rankings). Pick combinations when order does not matter (e.g., lottery tickets, committees).

What if r > n?

Without repetition, that’s invalid (you can’t choose more distinct items than exist). With repetition allowed, it’s fine.

Why do I see huge numbers?

These counts grow very quickly; we show both the exact integer and an approximate scientific notation like \(1.23 \\times 10^{45}\).

Is my data private?

Yes—everything runs entirely in your browser.