We were covering some elementary combinatorics in the Pre-Calculus course this past week and were discussing some problems from VK Balakrishnan’s Discrete Mathematics textbook. I took a Discrete Math course at University of Maine in 2000 from Balakrishnan and really enjoyed the class.

I needed to make a quiz question for the Pre-Calculus class and tried to remember some of the more interesting ways Balakrishnan had constructed his problems and came up with this one:

Seven people (A, B, C, D, E, F, G) want to ride into Portland but the car will only hold four. Person “A” owns the car and will always be driving. People “F” and “G” don’t get along and won’t ride together. If it makes no difference where in the car people sit, how many ways are there for four people to ride into Portland together?