## Problem of the Day #45: Pre-Arranged AbsencesMay 3, 2011

Posted by Arjun in : potd , trackback

Albert has decided that he needs to cram for AP exams. For that purpose he has decided to take pre-arranged absences on strategic days. In this hypothetical situation he is taking AP Chemistry and Psychology on Monday, Calculus BC on Wednesday,  Biology and Physics B the next Monday, and World History and Human Geography on the next Thursday and Friday, respectively. A maximum of $3$ half days is allowed, and they can only be taken:

• after or before a specific exam on a day
• directly before or after consecutive exam days (either morning or afternoon)
• directly before or after a double exam day

What is the number of combinations of absences Albert can take?