programmingnoob

so I have to write a reg expression for
the set of strings whose first character is a and ends in either a
or ac. In the middle the strings have any combinations of b's and c's,
including no b's nor c's.

Now, what I came up with is
{a}.{b, c}*.{a, ac}

apparently, this is not right (my solution doesnt match with the answer given) Now, can you tell me what you see wrong in my solution?