Answer:
4,536
Step-by-step explanation:
Ok so lets write down any old 4 digit number
abcd
How many choices do we have for the digit a? We have 9 choices (since the first digit cannot be 0). Now for each possible choice of a we have 9 choices for b (since we want b to be a different digit to a and we now allow 0).
So for choice of the ab part we have 9∗9=81 possibilities.
Now for each of these we have 8 choices for c (to avoid c being the same as either a or b). And for each of these we have 7 choices for d (to avoid d being the same as either a,b or c).
So in total there are 9∗9∗8∗7=4536 possible numbers.
