Mathematics Problem Of the Week

Spring 2008

POW #3

 

POW Assignment Lottery

 

   I need to choose faculty to write POW problems for the next n weeks.  Having a strong belief in the random process, I decide to put n different faculty names in a hat.  The first name drawn writes the problem for week #1, but I want to keep it very random so I’ll put his/her name back in the hat for the next draw (so they could be chosen again and someone might not be chosen at all).  To avoid a mutiny, I won’t assign any person more than twice, so a name is not returned to the hat after being drawn a second time.

(a) Suppose we use n=3 weeks and the faculty are named A, B and C.  In how many different ways could POW assignments be made if nobody does more than two problems (and order matters so ABB¹BAB)?

(b) What if we have n=7 weeks and 7 faculty?  Justify your answers.

 

 

Due Friday, February 15^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.