A: This problem can be broken down into two parts.
- You find the total number of digits in the single-digit numbers which is 9
- For the double-digit numbers, the largest number is 99. So you subtract the single digit numbers from the total numbers which is 90. Therefore, you have 90 double-digit numbers. 90*2 = 180
Answer (a): 189
B: There are 9 numbers containing a zero (10, 20 ... 90). They each only have one zero therefore there are 9 zeros. The total number of digits is 189 so you have 9/189 which can be simplified to 1/21
Answer (b): 1/21
C: Each digit appears once in the single-digit numbers. Then for the next 8 "tens" they appear once in 7 of the "tens" and 9 times in one "tens" category. For example, 9 appears once in the 10's (19) but appears 9 times in the 90s (91, 92...). Therefore, each digit appears 17 times. So you have (17*1)+(17*2)...(17*9) which should amount to 765.
Answer (c): 765
