There are n≥3 job openings at a factory, ranked 1 to n in order of increasing pay. There are n job applicants, ranked from 1 to n in order of increasing ability. Applicant i is qualified for job j if and only if i≥j. The applicants arrive one at a time in random order. Each in turn is hired to the highest-ranking job for which he or she is qualified AND which is lower in rank than any job already filled. (Under these rules, job 1 is always filled, and hiring terminates thereafter.) Show that applicants n and n \minus{} 1 have the same probability of being hired. probabilitycombinatorics unsolvedcombinatorics