Assignment:
A representative is to be selected from each of 3 departments in a small college. There are 7 people in the first department, 5 in the second department, and 4 in the third department.
a. How many different groups of 3 representatives are possible? 3360
b. How many groups are possible if any number (at least 1) up to 3 representatives can form a group? (Each department is still restricted to at most one representative.)
Provide complete and step by step solution for the question and show calculations and use formulas.