Question

Question #15a8c

Answer 1

Let's say that a three-digit number starting with 0 is a two-digit number, so no leading zero

Explanation:

(1)
1st digit: 5 choices (no 0)
2nd digit: 5 choices
3rd digit: 4 choices
For a total of `5xx5xx4=100`

(2)
Here we work the other way around:
3rd digit: 3 choices (1, 3 and 5)
1st digit: 4 choices (5 choices left but no 0 allowed)
2nd digit: 4 choices
For a total of `3xx4xx4=48`

(3)
(a) 1st digit is 3:
2nd digit: 2 choices (4 or 5)
3rd digit: 4 choices
For a total of `2xx4=8`
(b) 1st digit is 4 or 5 (=2 choices)
2nd digit: 5 choices
3rd digit: 4 choices
For a total of `2xx5xx4=40`
Grand total `8+40=48`

Note:
If 0 as a leading digit is allowed, the answers to (1) and (2) would be `120` and `60` respectively (figure that out).