Latin Squares

1. How many different experiment schedules are there for the problem:

Design the structure for an experiment that would enable a comparison of 3 drugs using 3 different groups of 10 people each. Make sure that each drug is tested during each of the 3 40-day trials and that each drug is tested on each group of volunteers. The structure you make should enable anyone to see at a glance which drug is administered to any of the 3 given groups during any of the 3 given periods of time.

2. Suppose that there are 4 drugs, 4 groups of volunteers, and 4 40-day trials; how many experiment schedules are there now? How about for n drugs, n groups of volunteers, and n 40-day trials?