Stage 1 - Selecting from 9 digits I get (0-9)
Stage 2 - Selecting from 10 digits - Little lost here . Since one digit is already selected in stage 1 - Shouldnt it be 9 digits to select from ?

Digits such as 999 and 444 are also palindromes.

So for the first place there are 9 options namely (1,2,3,4,5,6,7,8,9) and second digit has 10 options (0-9).

There are two situations:

1. xyx (ex: 101, 121..)
2. xxx (ex: 111, 2222..)

For the first case:

xyx: The hundredth position can be taken by any one among the nine digits..(1,2,3...9)
The tenth position can be any one among the nine numbers (0,1,2..9 except the digit which we have taken in the hundredth position)
The unit's place should be the same digit which we assigned in hundredth position.
Hence this can be arranged in 9 * 9 * 1 = 81

For the second case:

xxx: The hundredth position can be taken by any one among the nine digits..(1,2,3...9)
The tenth and the units's place should take the same digit which we assigned in hundredth position.
Hence this can be arranged in 9 * 1 * 1 = 9

The total number of palindromes between 100 and 1000 = 81 + 9 =90.

ANSWER: 90

From 100 - 200 there is 10 palindromes. Those are 101,111,121,131,141,151,161,171,181,191.
As we can see when the first and third digit matches, it is a palindrome.
Similarly 201-300 there is 10 Palindromes.
301-400 there is 10 palindromes.
So in total 100-1000 there is 10*9 = 90 palindromes.

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