Einstein's Zebra Riddle normally has 5 people;

5 house numbers;

5 colours;

5 nationalities;

5 drinks;

5 smokes;

And most importantly, 5 pets.

If we already know the house numbers, colours, nationalities, and drinks each person has, how many ways are there to assign the remaining two types of traits within the 5 people?

No two people must have the same trait, and assume people are distinct. For instance, Alice with Kools and a Zebra is different from Bob with Kools and a Zebra.