If I were a combinatorics professor...

Combinatorics is the mathematical study of arrangements, selection, distributions, etc. Basically it boils down to "counting" how many ways you can do something. For example, how many ways can you seat 7 people in a line of 5 chairs? Or, how many ways can you pick 4 jellybeans from a bag containing 3 red ones, 4 blue ones, and 5 black ones, if you must have at least one of each color? These are the things combinatorics is interested in. These are the types of questions we are given.

These are... boring and lifeless.

If I were teaching a class of combinatorics, my questions would be vivid and funny! They wouldn't be boring.

For example:

1. James's belt is getting a little old. It is a little frayed and ragged. James estimates that he can get only 5 more spankings out of the belt before it breaks. In how many ways can James dispense swift and severe punishment to his 3 children?

2. a) How many ways can you seat 8 people at a round banquet table?

b) How many ways can you seat 8 people at the same table if Mary has found out that her husband Jim has been sleeping with her sister, and because of this she refuses to sit directly next to or directly across from Jim?

3. Brad's dealer has 7 types of drugs for sale. If it takes 5 hits of any combination of drugs to make Brad pass out, in how many ways can Brad stone himself to unconsciousness this Friday? Assume that the order the drugs are taken in matters.

4. Seven couples show up at a swingers party. In how many ways can the 14 people be paired off if at most 2 men can be matched up with their own wife?


Aren't these much better and much less boring?


ALSO: Bonus points to anyone who can answer these in the comments!