Question

A president and a vice president for a student organization are chosen from seven people. How many different president/vice president combinations are possible?

Answer 1

Yay, it’s 42, I would think that it’s 49 cause that’s 7 squared but...

Answer 2

Answer: 42

There are 7 choices for the president, then after the president is selected, there are 6 choices left for VP. This gives 7*6 = 42 different permutations.

Order matters because of the different office titles. If we just wanted two people regardless of ordering, then we would divide by 2 to get the combination value. However, we want the permutation value in this case.