Draft:Bpow1997-18

One of the American states runs lottery in which players select five numbers from between 1 and 32 (inclusive). Each player may choose the numbers of their own liking or allow the computer that prints out the ticket to randomly select the five numbers. At a convenience store which sold the tickets, and where I had stopped for gas, the clerk had just bought one of these randomly generated tickets. She took a look at it and, seeing that her ticket contained a consecutive pair of numbers, reasoned that it would never be a winning ticket and discarded it. Leaving aside that fact that any ticket could be a winner, was she right in doing so? More precisely, what is the probability that five numbers selected at random, uniformly and without replacement, from between 1 and 32 will contain a consecutive pair?

Note that 1 and 32 are not a consecutive pair.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.