Three dice are rolled what is the probability that the numbers shown will all be different

A standard six side die is rolled three times.

Find the chance that three different faces appear?

My thoughts:

Probability p (same face pops up is) = 1-P

. You roll first one and record what you get. The probability of next (2) two rolls give you same face is ... ? My chances of rolling any given face is 1/6

. It does not matter what you get first role the next two rows have to the same as the first one role. Therefore = (1 - (1/6) 2) = 1-