Q:

How to calculate possible permutations with varying constraints

I have created a random email generator.  The email is put together with the following format:
(random first name) (random separator) (random last name) (random integer) @ (random domain)
150 possible first names;
3 possible separators;
150 possible last names;
Integer between 0 and 110;
15 possible domains
I created this for a side project and then out of curiosity wanted to calculate the possible permutations but soon found that this is more difficult that I first thought.  Can anyone find the answer and explain how you came to that answer?

A:

It seems like all the choices can be made independently, so the number of possible ways to form an email is the product of the ways to choose each thing. So this is 150*3*150*10*15. 
See this wiki article on the multiplicative principle or these notes (under principle of counting). 

