There are 10 applicants for a job, labeled 1, 2, ... , 10. Their suitability for the job is ranked in this order (so 1 is more suitable than 2, who is more suitable than 3 and so on). But an applicant's ability is only measured when they are interviewed. They are interviewed in the order a1, a2, ... , a10. The first three interviewed are automatically rejected. Thereafter if an applicant's suitability is better than that of all previous applicants they are accepted (without interviewing the other applicants). If the first nine applicants interviewed are not accepted, then the tenth is automatically accepted. Let ni be the number of permutations a1, ... , a10 which result in applicant i getting the job. Show that n1 > n2 > ... > n8 = n9 = n10. Show that the probability that one of 1, 2, 3 gets the job is over 70% and that the probability of one of 8, 9, 10 getting the job is not more than 10%.
-
UP 0 DOWN 0 0 0
