Before you go any further, I would like you to know that I'm not the best at math, so my answers might be wrong.

a) If it starts at 1 and goes to 99, we know that the answer is 99 numbers. (Even you should be able to figure this one out).

Wait wait wait, but if we count each digit seperately, then it would actually be 189 digits (look below for how)

b) I have two answers for this, if you mean that one of the digits as in we count 10 as a digit, then there would be no probability for Sam to pick a 0, because there's no 0's on the list.

The other option is we count 10 as a 1 and a 0. In this case we have 10, 20, 30 to 90, and thus we have 9 0's. The total number of digits is:

1-9 (9 digits)

10-99 (180 digits)

Total: 189 digits

And we have 9/189 = 1/21

c) The sum of all the digits hmmmmm. Again, I don't know if digits mean each integer seperately or to split an integer. But, if it's the first one, then there are 99(99+1)/2 = 50 * 99= 4950 digits ( I tink).

The other option is splitting each integer, and for this, there's an easy way we can do this. (I think).

First we note how many 1's we have (1,10,11,12,13,14,15,16,17,18,19,21,31...91) Altogether, that is 19 1's (Check that if I counted wrong). So that is 19 of each number. So we have the following:

19 * 1 + 19 * 2 + 19 * 3 + 19 * 4 + 19 * 5 + 19 * 6 + 19 * 7 + 19 * 8 + 19 * 9 = 855

Hope those answers are correct, be sure to tell me if they're wrong...