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−