- #1

roam

- 1,271

- 12

## Homework Statement

How many (natural) numbers less than 100 contain a 3? (Note: 13, 35 and 73 all

contain a 3 but 42, 65 and 88 do not).

## The Attempt at a Solution

Of course I know that the numbers containing a 3 including 10 numbers starting with a 3 (30, . . . 39),and 10 numbers ending in a 3 (3, 13, . . . , 93), with 33 being counted twice, so a total of 19 numbers. I've found this by counting. But is there a quick systematic way of obtaining this answer

**using combinations/permutations**etc? Unfortunently my knowledge of combinatorics is very poor, so I appreciate any help.

Between 10 to 100 there are 98 2-digit numbers that can possibly contain a 3 in the 1's or 10's positions... I'm stuck here.