Final answer:
There are 9,000 distinct digits between 1000 and 9999.
Step-by-step explanation:
The distinct digits between 1000 and 9999 can be calculated using the concept of permutations. Since the numbers are 4 digits long, there are 4 positions to fill. The first position can be filled with any digit from 1 to 9 (since 0 cannot be the leading digit in a number). The remaining three positions can be filled with any digit from 0 to 9 (including 0). Therefore, the total number of distinct digits between 1000 and 9999 is 9 * 10 * 10 * 10 = 9,000.