WOW! How Do They Do That?

Team: 
The Unknowns
Topic: Probability, Counting & Combinatorics
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How to solve problem 140: If a room has seven doors, in how many ways can a person enter through one door and exit through another door?

Common Core Standards: 7.SP.8
Problem #: 
140 (2011-2012)
Problem Difficulty Level: 3 [?]