Combination and Permutation Calculator
nCr, nPr and factorials for counting problems.
Enter your values
Enter the total items (n) you are working with.
Enter the chosen (r) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)!)
At a glance
| What it does | nCr, nPr and factorials for counting problems. |
|---|---|
| Category | Math |
| Inputs needed | Total items (n), Chosen (r) |
| Main output | Combinations (nCr) |
| Formula | nCr = n! ÷ (r!(n−r)!) |
| Cost | Free — no sign-up, no download |
How to use the Combination and Permutation Calculator
- 1Enter the total number of items.
- 2Enter how many you are choosing.
- 3Read combinations and permutations.
Inputs explained
- Total items (n)
- Enter the total items (n) you are working with.
- Chosen (r)
- Enter the chosen (r) you are working with.
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.
What do I need to enter into the Combination and Permutation Calculator?
Just 2 values: total items (n), chosen (r). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Combination and Permutation Calculator work out the answer?
Combinations count selections where order does not matter (nCr); permutations count arrangements where it does (nPr). It applies the formula nCr = n! ÷ (r!(n−r)!) and shows the working so you can check each step by hand.
Is the Combination and Permutation Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.