Valid Clock Time Combinations

Question

You get four integers A, B, C and D, each one a single digit. Put them on a 24-hour digital clock in the form "HH:MM" so that each of the four fills one of the four positions (no digit left out, none used twice), and count how many different times you can show this way. A time counts only if it falls between "00:00" and "23:59", both included. When two arrangements of the digits show the same time, that time is counted once. ...