Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
Solutions Due: Friday, September 8, 5:00 p.m.
Send solutions to firstname.lastname@example.org.
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award.
Luxury in the Air
An airplane has 100 rows of seats, with two seats in each row. Passengers are assigned seats at random. If you are one of 100 passengers getting on the airplane, what is the probability that you will have a row all to yourself? Answer, and explain.
Can you generalize to the case of N rows and K passengers? Can you generalize to the case of N rows, K passengers, and M seats in each row?