There cannot be any 4-digit numbers, since 1 is not allowed for a first digit.

So they are all 3 digit numbers.

We can choose the first digit any of 3 ways {5,6,7} (can't be 0).
We can choose the second digit any of the 5 remaining ways (can be 0).
We can choose the third digit any of the 4 remaining ways.

That's 3*5*4 = 60 ways.

Edwin