# Order preserved Lotto distribution

42 balls are numbered 1-42. You select six numbers between 1 and 42. (The ones you write on your lotto card). I know if it is randomly selected regardless of order, it is easy to compute probability that they contain some numbers of yours, E.g. P(Match 4), by hypergeometric Distribution. BUT, NOW, the point is what is probability of matching 4 numbers, given that order is preserved? E.g. If we write 10 at first next number must be more than 10 (cant write 9 after 10).

Thanks in advance for your attention. Please be advised it is Not homework.

## Answers and Replies

I don't fully understand the question. If you picked a 42 first then you would blow up? There seems to be inconsistencies in the question.

Ray Vickson
Science Advisor
Homework Helper
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42 balls are numbered 1-42. You select six numbers between 1 and 42. (The ones you write on your lotto card). I know if it is randomly selected regardless of order, it is easy to compute probability that they contain some numbers of yours, E.g. P(Match 4), by hypergeometric Distribution. BUT, NOW, the point is what is probability of matching 4 numbers, given that order is preserved? E.g. If we write 10 at first next number must be more than 10 (cant write 9 after 10).

Thanks in advance for your attention. Please be advised it is Not homework.

So much here depends on how you choose to define the probability distribution over ordered samples; that is: to say what you mean by a random ordered sample. One way would be to take an unordered sample, then sort it, but there are other methods as well. In the case of sorting an unordered sample the probability of getting a match would be the same as in the unordered case, because the same set of numbers would be involved.

RGV