Hi abhasjha,

These types of questions are always carefully written, so you have to pay attention to the details and you have to think about the limitations for each digit.

For example, a 6-digit number won't start with a 0, but the other digits could be 0 (unless it's a numerical code, then it MIGHT be able to start with a 0). Here, I'll assume that the intent is to ask for a 6-digit number with no special rules to consider besides the ones that you listed....

The possible 6-digit numbers are 100,000 - 999,999, inclusive, so there are 900,000 possible numbers.

We're asked for the probability of finding a very specific type of 6-digit number

1st Digit: 1-9 = 9 possibilities
4th Digit: MUST match the 1st = 1 possibility (once we know the first digit)
2nd Digit: 0-9 = 10 possibilities
5th Digit: MUST match the 2nd = 1 possibility (once we know the second digit)
3rd Digit: 0-9 = 10 possibilities
6th Digit: MUST match the 3rd = 1 possibility (once we know the third digit)

So....(9)(10)(10)(1)(1)(1) = 900 possibilities that match the description

900/900,000 = 1/1,000 = the probability of finding the 6-digit number described.

GMAT assassins aren't born, they're made,
Rich