Lottery Combinations Calculator

How it is calculated

total is the size of the pool of numbers and pick is how many are drawn. Order does not matter and no number repeats, so the count is the binomial coefficient:

C(total, pick) = total! ÷ (pick! × (total − pick)!)

The tool does not compute the factorials. It multiplies and divides step by step, result = result × (total − r + i) ÷ i for i = 1 to r, where r is the smaller of pick and total − pick, in exact whole-number arithmetic. The odds are shown as 1 : C. Both inputs must be whole numbers of at least 1, and pick cannot exceed total. The count is printed with every digit or not at all: results up to about 9.2 × 10¹⁸ are exact (33 from 66 gives 7,219,428,434,016,265,740), and anything larger, such as 34 from 67, shows no result instead of rounded digits. Only the main-draw jackpot is covered: bonus balls, star numbers and lower prize tiers are not included.

Common mistakes

• Counting orderings. A draw of 3, 14, 22, 30, 41, 55 is the same ticket as 55, 41, 30, 22, 14, 3; the tool does not multiply by the number of orderings.
• Using the tool for games that draw from two pools, such as five main numbers plus two stars. Enter each pool separately and multiply the two counts yourself.
• Reading 1 : 45,057,474 as meaning you will win once in that many tickets. It is the chance per ticket, and each draw is independent.
• Entering the bonus ball as part of the pick count. If a game draws 6 plus a bonus ball, the jackpot odds here use only the 6.
• Entering a pick larger than the pool (6 from 5), or a fractional number. Both show no result, as does a very large pool and pick such as 20 from 100 whose count is past the exact limit.