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Unformatted text preview: 3.1. PERMUTATIONS 89 7 Five people get on an elevator that stops at five floors. Assuming that each has an equal probability of going to any one floor, find the probability that they all get off at different floors. 8 A finite set Ω has n elements. Show that if we count the empty set and Ω as subsets, there are 2 n subsets of Ω. 9 A more refined inequality for approximating n ! is given by √ 2 πn n e n e 1 / (12 n +1) < n ! < √ 2 πn n e n e 1 / (12 n ) . Write a computer program to illustrate this inequality for n = 1 to 9. 10 A deck of ordinary cards is shuffled and 13 cards are dealt. What is the probability that the last card dealt is an ace? 11 There are n applicants for the director of computing. The applicants are inter- viewed independently by each member of the three-person search committee and ranked from 1 to n . A candidate will be hired if he or she is ranked first by at least two of the three interviewers. Find the probability that a candidate will be accepted if the members of the committee really have no ability at all to judge the candidates and just rank the candidates randomly. In particular,to judge the candidates and just rank the candidates randomly....
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This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.
- Spring '09