How many 3's appear from 1 to 500?

Instead of going from 1 to 500, let's just subtract one from the set and come up with "How many 3's appear from 1 to 499?"

Total possible combinations in this, including leading zeros, is 5*10*10, i.e. 5 possible in the first set(0,1,2,3,4), and 10 in the second two(0,1,2,,4,5,6,7,8,9).

Instead of figuring out how many have a 3, lets figure out how many don't. Well there is 4 possibilities in the first (0,1,2,4), and nine in the second two (0,1,2,4,5,6,7,8,9).

So, total = 5 * 10 * 10 = 500

Without 3 = 4 * 9 * 9 = 324

500-324 = 176

There are 176 numbers from 1 to 500 that have the digit 3 in them.