Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

To win a lottery, you must pick the winning 3 numbers from the integers 1-9 (no repeat numbers). What is the probability of winning the lottery by choosing the correct 3 numbers?

I think its a combination problem. I got 84 for the answer but I'm not sure.

share|cite|improve this question

If you just have to get the right three numbers, in any order, then you’re right: it’s a combination problem, and there are $\binom93=84$ possible sets of three numbers. However, that’s not the answer: you want the probability of picking the right one of these $84$ sets, which is $\frac1{84}$.

If the order does matter, you have $9$ ways to pick the first number, $8$ to pick the second, and $7$ to pick the third, for a total of $9\cdot8\cdot7=504$ possibilities, and your probability of winning shrinks to $\frac1{504}$.

share|cite|improve this answer
Beat me to it, here's +1 – World Engineer Feb 9 '13 at 23:08

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.