Question

Find the number of positive integers with distinct digits?​

Answer 1

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In any event, once the strings have eleven digits they can't all be distinct (pigeonhole property, since we are in base 10) so the numbers to be dealt with here are relatively small for a computer. (In other words, even a poorly written program should run pretty quickly.)

Answer 2

Answer:

The answer is 60. The Op did not say that the any of the five digits given could be used more than once in any given three digit number.