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?
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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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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