If you do it for long enough you are certain (or at least with probability 1)

to get duplicates.

There is an ambiguity in you question, drawing 7 digits at random from

a set of 20 does not guarantee that you get a 7 digit number. The

digit drawn for the most significant position in the 7 digit number may be a

zero, which gives at most a six digit number.

I expect there are more side conditions that you need to add to this

question before you have pinned down your real question.

Note each of {0, 1, 2, ...9} in your set of 20 digits does not occur with

equal probability as the leading digits of your 10 digit numbers cannot be zero).

RonL