# Is this a Permutation or a Combination?

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.

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## 1 Answer

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 $\frac1{504}$.

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Beat me to it, here's +1 –  World Engineer Feb 9 '13 at 23:08