First we calculate the sum of all possible 3 digit numbers with 6 digits 0,1,2,3,4,5, allowing 0 also to be the first digit.
- There are 6x 5 x 4 = 120 numbers.
- The digits are evenly dispersed, so each digit appears 120/5 = 24 times in the 100's place,10th place and unit place.
- Summing the 100's place numbers, we get 24 * (0+1+2+3+4+5) * 100 = 24*15*100= 36000.
- Summing the 10's place numbers, we get 3600; 10's.
- 1's place, 360.
- Adding together, 39960.
Now we have to subtract the numbers start with 0.
- They have a 0 in the 100's place and a digit from 1 to 5 in each of the other 2 places.
- There are 5x4 = 20 of them.
- Again 5 digits are distributed evenly, each one appearing 20/5 = 4 times
- so the sum in the 100's place is 4 * (1 + 2 + 3 + 4 +5) * 10 = 600; the sum in the 1's place is 60.
- Adding together, 6600.
Subtracting the second sum from the first sum we get a final answer of 39960 - 6600 = 39300