Problem of the Week

Because of the upcoming FALL BREAK, this problem will remain posted for two weeks.

This problem was suggested by Bradley University mathematics alumnus (and track athlete)  Matt Occhipinti.

 Six schools each send their two top runners to a track meet.  The twelve runners are assigned, at random, two runners to a lane on a six-lane track.  What are the chances that at least one school will have both of its runners assigned to the same lane?

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ã2003 Alberto L. Delgado