How many three-digit numbers that are divisible by 5 have all three digits different?

Explanation

1. 01

   Split by the units digit, since the rule for 0 changes with it.

2. 02

   Units digit 0: hundreds digit has 9 choices, tens 8, so $9 \times 8 = 72$.

3. 03

   Units digit 5: hundreds digit cannot be 0 or 5, so 8 choices; tens then has 8 choices (0 is allowed), so $8 \times 8 = 64$.

4. 04

   Total $= 72 + 64 = 136$.