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.
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.