Combination and Permutation Calculator
nCr, nPr and factorials for counting problems.
Enter your values
Results update instantly as you type — no submit needed.
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.
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.