Let’s discuss thecommonly understood lottery game.

If we draw out six numbered balls from forty-nine, order makes no difference.

Only content matters. The combination {2,4,27,33,41,42} is the same as {41,2,33,4,27,42}. If the first is the winning combination then so is the second.

is the number of possible winning combinations.

However, if you note that example contains a pair of consecutive numbers, 41 & 42. That is what you do not want. Well sometime ago some players, in I think Louisiana, noticed that quite often winning combinations did have consecutive pairs. They want to file a legal complaint. But as it turns out it not that unreasonable for it to happen.

We can think of that a string of six ones and 43 zeros as one ticket. Any arrangement of that string could represent a winning combination. So your question comes down to how many rearrangements of that bit string have no two consecutive ones. The answer is the zeros create 44 places to put the ones. So for this particular set of numbers there almost a 50/50 chance a winning ticket will have consecutive entries.

Now of course, if your own lottery game turns on theorder in which the balls come out of the hopper, then a totally different analysis must be done. But in the usual lottery order does not matter.