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Calculation Machine

Combination and Permutation Calculator

nCr, nPr and factorials for counting problems.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Combinations (nCr)
2,598,960
Permutations (nPr)
311,875,200
With repetition allowed
380,204,032
Probability of one specific combination
1 in 2,598,960

Working

  1. 152C5 = 52! ÷ (5! × 47!) = 2,598,960

Quick answer

Combinations count selections where order does not matter (nCr); permutations count arrangements where it does (nPr).

The formula

nCr = n! ÷ (r!(n−r)!)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Total items (n)52
  • Chosen (r)5

Result

  • Combinations (nCr)2,598,960
  • Permutations (nPr)311,875,200
  • With repetition allowed380,204,032
  • Probability of one specific combination1 in 2,598,960

How to use the Combination and Permutation Calculator

  1. 1Enter the total number of items.
  2. 2Enter how many you are choosing.
  3. 3Read combinations and permutations.

Frequently asked questions

When do I use permutations?

When order matters — race podiums, PINs and seat arrangements. Lottery draws and committees use combinations.

Why is 52C5 so large?

There are 2,598,960 possible five-card poker hands, which is why specific hands are rare.

About this calculator