Five friends—Allison, Beth, Carol, Diane, and Evelyn—have

QUESTION:

Five friends—Allison, Beth, Carol, Diane, and Evelyn—have identical calculators and are studying for a statistics exam. They set their calculators down in a pile before taking a study break and then pick them up in random order when they return from the break. What is the probability that at least one of the five gets her own calculator? [Hint: Let A be the event that Alice gets her own calculator, and define events B, C, D, and E analogously for the other four students.] How can the event (at least one gets her own calculator} be expressed in terms of the five events A, B, C, D, and E? Now use a general law of probability. [Note: This is called the matching problem. Its solution is easily extended to n individuals. Can you recognize the result when n is large (the approximation to the resulting series)?]