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?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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
are present.
c) Who is the "essential executive" without whom the safe cannot be opened?
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