Combination and Permutation Calculator
nCr, nPr and factorials for counting problems.
Enter 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
- 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).
nCr = n! ÷ (r!(n−r)!)
How to use the Combination and Permutation Calculator
- 1Enter the total number of items.
- 2Enter how many you are choosing.
- 3Read combinations and permutations.
Worked example
Using the values the calculator loads with:
Inputs
- Total items (n)52
- Chosen (r)5
Results
- Combinations (nCr)2,598,960
- Permutations (nPr)311,875,200
- With repetition allowed380,204,032
- Probability of one specific combination1 in 2,598,960
- 52C5 = 52! ÷ (5! × 47!) = 2,598,960
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
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.