How to use the Possibility & Combination Calculator
- Enter the total number of items n (for example 49 lottery numbers) and how many are chosen, r (for example 6).
- Read all four results: combinations, permutations, and both versions with repetition. Pick the one that matches your question — does order matter, and can items repeat?
- Hover or open “Exact value” to see huge results digit by digit.
- Use How many possible codes? for PINs, lock codes and passwords.
Which formula do I need?
| No repetition | With repetition | |
|---|---|---|
| Order matters | Permutations: n! / (n−r)! | nʳ (PINs, passwords) |
| Order doesn’t matter | Combinations: n! / (r!(n−r)!) | (n+r−1)! / (r!(n−1)!) |
Ask two questions: does the order matter? (a podium does, a lottery ticket doesn’t) and can an item be used more than once? (a PIN can repeat digits, a lottery draw can’t).
Examples
- Lotto 6 of 49: C(49, 6) = 13,983,816 — the odds of the jackpot are 1 in about 14 million.
- Poker hands: C(52, 5) = 2,598,960 different 5-card hands.
- 4-digit PIN: 10⁴ = 10,000 possibilities (order matters, digits repeat).
- Gold, silver, bronze among 8 runners: P(8, 3) = 336.
- Ice cream: 3 scoops from 10 flavours (repeats allowed, order irrelevant): C(12, 3) = 220.
Big numbers, exact
Factorials grow incredibly fast — 70! already has 101 digits. The calculator uses arbitrary-precision integers, so results stay exact instead of turning into rounded floating-point numbers. For password security, possibilities translate directly into cracking time — see the Password Strength Checker. For simple ratios and percentage changes use the Percentage Calculator, and for random draws the Random Number Generator.
Tools that pair well with the Possibility & Combination Calculator
- Number Base Converter — Type a number in any base and see it in all the others instantly.
- Unit Converter — Convert between metric, imperial and technical units in ten categories — with a two-way converter and a table of every unit at once.
- Age Calculator — Enter a date of birth to get the exact age in years, months and days — plus total days and weeks lived, the weekday you were born on, a countdown to the next birthday and your star sign.
- Date Difference Calculator — Count the days between two dates — including business days and a years/months/days breakdown — add or subtract time from a date, or run a live countdown.
Frequently asked questions
What is the difference between combinations and permutations?
Permutations count arrangements where order matters (ABC ≠ CBA). Combinations count selections where order doesn’t matter (ABC = CBA), so there are always fewer combinations than permutations.
What does nCr mean?
“n choose r” — the number of ways to pick r items from n without caring about order: n! / (r! × (n−r)!). It’s also written C(n, r) or as a binomial coefficient.
How many combinations does a 4-digit code have?
10,000 (0000 to 9999), because each of the 4 positions can be any of 10 digits: 10⁴. A 6-digit PIN has 1,000,000.
What are my odds of winning the lottery?
For a draw of 6 numbers from 49, there are 13,983,816 combinations, so one ticket has a 1 in 13,983,816 chance. Games with an extra bonus number multiply this further.