Problem of the Week

PROBLEM 212

Because of the upcoming Spring Break, this problem will remain posted for two weeks.  Enjoy the break!

During a recent visit to Las Vegas I had the opportunity to play the game of Keno in which each player chooses 28 out of 80 possible numbers on a board.  After all players have made their selections (and paid!), the casino then chooses its 28 numbers at random.  The payoff is determined by the number of times your numbers match those chosen by the casino.  At one particular casino they paid out (to various degrees) unless you had exactly three, four, or five matches.  What is the probability that you will lose your bet by matching exactly three, four, or five numbers?

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ã2005 Alberto L. Delgado