dice - Probability of rolling a "1" on a die conditioned on when all rolls are different.

So I have this problem:

I am rolling a six sided die 3 times.

Conditioned on the rolls all being different, what's the probability at least one die is a "1"

So I worked it out like this:

probability of not getting a 1 on the first roll is 5/6

probability of not getting a 1 on the second roll is 4/6

probability of not getting a 1 on the second roll is 3/6

I then just did (5/6) * (4/6) * (3/6) to get 60/216 possible conditions where you would not roll a 1.

Doing 216-60 you get that 158/216 possible solutions (or 13/18) possible solutions for rolling a "1" when all numbers are different. Does this make sense? The number seems a bit large and I am not sure how to check it.

Thank you in advance.

Answer

You're almost there, but you made a small error:

Hint: How many possible outcomes are there on the second roll?