Using the digits 1, 2, 3 and 5, how many 4 digit numbers

Using the digits 1, 2, 3 and 5, how many 4 digit numbers can be formed if

a) The first digit must be 1 and repetition of the digits is allowed?

b) The first digit must be 1 and repetition of the digits is not allowed?

My thinking:

a) chose 1 then 2,3,5 can have 3^3 ways to form numbers. The answer is 27


b) chose 1 then 2,3,5 can have 3! ways to form numbers without repeating numbers. The answer is 6.

Am I right?

Thanks mmm.

I think you are right.