Lotteries, scratchcards and bingo
How do I calculate the odds of winning a six-from-45 lottery?
Direct answer
For a fair six-from-45 lottery there are 45 choose 6 = 8,145,060 distinct combinations; one valid combination has jackpot probability 1/8,145,060 (≈0.00001228%).
How to use this answer
This answer is based on the mathematical principle or published rule identified in the source below. If the question involves a live betting market, confirm its settlement definition before applying it to a specific bet.
There are C(45,6)=8,145,060 equally likely six-number combinations, so a specific ticket has one-in-8,145,060 jackpot odds.
Use the published game matrix and prize rules for the exact lottery or scratchcard. Identical tickets, rollover jackpots and claimed win patterns should be assessed using probabilities rather than intuition.
Reference: lotterywest.wa.gov.au · published rules or source ↗