Odds that every number you picked gets drawn
When k items are drawn without replacement from a pool of n, the probability that all m items you specified are among them is C(n − m, k − m) / C(n, k). The probability that at least one is drawn removes the draws containing none of them: 1 − C(n − m, k) / C(n, k). Draw 6 from 45 with 6 numbers specified and only 1 of the 8,145,060 combinations matches, so the odds are 1 in 8,145,060, while at least one overlap happens 59.9435% of the time.
Combination counts grow fast, so the pool size is capped at 1,000 and combination counts are computed exactly with whole-number (BigInt) arithmetic down to the last digit, while probabilities are computed as floating-point values in log space. Counts longer than 30 digits are shortened to a power of ten marked with ≈. Every draw is assumed equally likely, and nothing drawn is returned to the pool.
Ordered permutations, draws with replacement and multi-tier lottery prize odds are not covered. Working out a win probability from a number of participants, or generating numbers to play, is not covered either. Written as of October 2026.
Frequently asked questions
There are 8,145,060 combinations, so the odds that all 6 of your numbers are drawn is 1 in 8,145,060.
By subtracting the share of draws that contain none of your picks from 1. For 6 of 45 with 6 picks it is 59.9435%.
No. It covers unordered combinations drawn without replacement only.