1. How many different three-letter words (including nonsense words) are there in which successive letters are different?
2. How many different outfits consisting of a coat and a hat can be selected from two coats and three hats?
3. How many different outfits can be selected from two coats, four hats, and two scarves?
4. A computer manufacturer assigns serial numbers to its computers. The first symbol of a serial number is either A, B, or C, indicating the manufacturing plant. The second and third symbols taken together are one of the numbers 01, 02, . . . , 12, indicating the month of manufacture. The final four symbols are digits. How many possible serial numbers are there?
5. Suppose that a license plate consists of a nonzero digit followed by three letters and then three nonzero digits. How many such license plates are there?