50. An absentminded professor wrote n letters and sealed them in envelopes without writing the addresses on them. Then he wrote the n addresses on the envelopes at random. What is the probability that exactly k of the envelopes were addressed correctly? Hint: Consider a particular set of k letters. Let M be the total number of ways that only these k letters can be addressed correctly. The desired probability is the quantity ; n k < M/n!; using Example 2.24, argue that M satisfies /n−k i=2 (−1)i / i! = M/(n − k)!.