A safe has 5 locks, v,w,x, y and z, all of which must be unlocked for the safe to open. The keys to the locks are distributed among five executives in the following manner: Mr.A has keys for locks v and x. Mr.B has keys for locks v and y. Mr.C has keys for locks w and y. Mr.D has keys for locks x and z. Mr.E has keys for locks v and z Find the answers of following parts using suitable method. a) Determine the minimal number of executives required to open the safe. b) Find all the combinations of executives that can open the safe. Write an expression f (A, B, C, D, E) which specifies when the safe can be opened as a function of what executives are present. c) Who is the "essential executive" without whom the safe cannot be opened?
A safe has 5 locks, v,w,x, y and z, all of which must be unlocked for the safe to open. The keys to the locks are distributed among five executives in the following manner: Mr.A has keys for locks v and x. Mr.B has keys for locks v and y. Mr.C has keys for locks w and y. Mr.D has keys for locks x and z. Mr.E has keys for locks v and z Find the answers of following parts using suitable method. a) Determine the minimal number of executives required to open the safe. b) Find all the combinations of executives that can open the safe. Write an expression f (A, B, C, D, E) which specifies when the safe can be opened as a function of what executives are present. c) Who is the "essential executive" without whom the safe cannot be opened?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A safe has 5 locks, v,w,x,y and z, all of which must be unlocked for the safe to open. The keys to
the locks are distributed among five executives in the following manner:
Mr.A has keys for locks v and x.
Mr.B has keys for locks v and y.
Mr.C has keys for locks w and y.
Mr.D has keys for locks x and z.
Mr.E has keys for locks v and z
Find the answers of following parts using suitable method.
a) Determine the minimal number of executives required to open the safe.
b) Find all the combinations of executives that can open the safe. Write an expression f (A,
B, C, D, E) which specifies when the safe can be opened as a function of what executives
are present.
c) Who is the "essential executive" without whom the safe cannot be opened?
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