SOLUTION: What is the probability that a randomly chosen four-digit number contains no repeated digits?

1.  The full space of events consists of 9999-999 = 9000 elements (4-digit numbers).



2.  Of them, the favorable sub-space are those 4-digit numbers that have no repeating digits.


        The number of elements in this sub-space = 9*9*8*7

            (any of 9 digits from 1 to 9 in the left-most position;   (0 (zero) is excluded);

             any of remaining 9 digits in the next position;   (0 is included !)

                  . . . and so on . . . 



3.  Hence, the probability under the question is   = 0.504 = 50.4%.