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Permutations & Combinations

nPr, nCr, factorials with exact BigInt math.

n (total items)

r (chosen items)

Permutations nPr

720

Combinations nCr

120

3628800

Formulas

nPr = n! / (n−r)! = 10! / 7! = 720
  (ordered arrangements of 3 from 10)

nCr = n! / (r!(n−r)!) = 120
  (unordered groups of 3 from 10)

Repeated permutations n^r = 1000
Repeated combinations C(n+r−1, r) = 220

Exact BigInt math — no precision loss even for huge values like 100P5.

About the Permutations & Combinations

Compute permutations and combinations with exact integer math: nPr for ordered arrangements, nCr for unordered groups, plain n factorial, plus the repeated variants n^r and C(n+r−1, r). BigInt arithmetic means results with dozens of digits print in full instead of overflowing into scientific notation.

How to use the Permutations & Combinations

Enter n, the total number of items.
Enter r, how many items are chosen or arranged.
Read the nPr and nCr tiles, and n! alongside them.
Open the Formulas box for the repeated-selection variants with your values substituted.

Permutations & Combinations FAQ

When do I use nPr versus nCr?

Use nPr when order matters — podium finishes, PIN codes, seating — and nCr when it does not: lottery draws, committees, card hands. The tool labels both interpretations in the output.

How large can the numbers get?

There is no artificial cap: values are computed as BigInt, so something like 100P5 shows every digit — the display truncates visually past 40 digits but notes the full length.

What do the repeated variants count?

n^r counts arrangements where items may repeat, like password characters, and C(n+r−1, r) counts multisets — selections with repetition allowed and no order.