A state lottery involves the random selection of six different numbers between 1 and 27. If you select one six number combination, what is the probability that it will be the winning combination?

Question

anonymous · Answer

First, I'm assuming that numbers are between 1 and 27 INCLUSIVE (meaning that both "1" and "27" are possibilities).

Next, since the question says that we're dealing with "different" numbers, then it must mean that we are dealing with random sampling WITHOUT replacement.

The last piece of information needed is whether or not the numbers represent an ORDERED or UNORDERED random sample (since the word "combination" appears, I'll assume we're dealing with UNORDERED samples). 

Which means that the total number of possible combinations is:

$$\left(\begin{matrix}27 \ 6\end{matrix}\right) =\frac{ 27! }{ (6!)(21!) } = 296,010$$

Which means that the probability of winning is about 0.00034%