Combination Calculator
Foundation content reviewed: . Verification scope is listed under Sources.
Mathematics describes probability; it does not predict winning numbers.
Count unordered selections
C(n,k) counts selections without replacement when order does not matter. This calculator accepts 1 ≤ n ≤ 1000 and 0 ≤ k ≤ n. Choosing zero items has one result: the empty selection.
Example: C(10,2) = 45.
Check a real lottery format
Pick a reviewed game to see its jackpot count built pool by pool. Pool sizes come from the LottoFlick registry; the Sources page lists what was verified.
Worked examples for the reviewed formats
Each row multiplies the count for the main pool by the count for any separate player-selected pool. Draw-only bonus or supplementary numbers are not chosen by the player and are not multiplied in.
| Game | Main-pool count | Separate-pool count | Jackpot combinations | Official jackpot odds (1 in N) |
|---|---|---|---|---|
| Powerball | C(69,5) = 11,238,513 | C(26,1) = 26 | 292,201,338 | 292,201,338 |
| Mega Millions | C(70,5) = 12,103,014 | C(24,1) = 24 | 290,472,336 | 290,472,336 |
| Eurojackpot | C(50,5) = 2,118,760 | C(12,2) = 66 | 139,838,160 | 139,838,160 |
| EuroMillions | C(50,5) = 2,118,760 | C(12,2) = 66 | 139,838,160 | 139,838,160 |
| Lotto 6/45 | C(45,6) = 8,145,060 | No separate pool | 8,145,060 | 8,145,060 |
| Loto 6 | C(43,6) = 6,096,454 | No separate pool | 6,096,454 | Not established |
| Loto 7 | C(37,7) = 10,295,472 | No separate pool | 10,295,472 | Not established |
| Oz Lotto | C(47,7) = 62,891,499 | No separate pool | 62,891,499 | 62,891,499 |
| Australian Powerball | C(35,7) = 6,724,520 | C(20,1) = 20 | 134,490,400 | 134,490,400 |
Count versus probability
A count is how many equally likely outcomes exist. For one exact valid ticket, the probability is 1 divided by that count. A number being called lucky does not change the count or how the draw is made.
Formula and interpretation
C(n,k) = n! / (k!(n−k)!). We calculate it by exact multiplicative BigInt arithmetic to avoid factorial overflow. C(6,6)=1, C(10,2)=45 and C(45,6)=8,145,060.
For one exact valid unordered selection in a fair uniform draw, probability is 1/C(n,k). Separate independent pools multiply: C(69,5) × C(26,1)=292,201,338. A draw-only bonus number does not automatically add another player selection pool.
What this tool cannot tell you
It does not calculate all prize tiers, ticket cost, tax, expected payout or the best numbers. Multiple distinct tickets in one draw cover different outcomes; buying duplicate tickets does not cover additional combinations. Across independent draws with fixed success probability p, the chance of at least one success in t draws is 1−(1−p)^t.