At local industry, the scheduler is facing adilemma. A shaft must go through the following threedifferent machining operations in order, and for eachof these operations there are several machinesavailable. The scheduler’s boss has asked him to list allthe different ways that the shaft can be scheduled.The scheduler is reluctant to begin the list becausethere are so many different permutations. Thefollowing information is available: Centering (4 machines)-part must go to two differentcentering machines, each set up with different tools Grinding (3 machines)-only one grinder is needed Milling (5 machines)-shaft must go through 3 differentmachines
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.
At local industry, the scheduler is facing a
dilemma. A shaft must go through the following three
different machining operations in order, and for each
of these operations there are several machines
available. The scheduler’s boss has asked him to list all
the different ways that the shaft can be scheduled.
The scheduler is reluctant to begin the list because
there are so many different permutations. The
following information is available:
Centering (4 machines)-part must go to two different
centering machines, each set up with different tools
Grinding (3 machines)-only one grinder is needed
Milling (5 machines)-shaft must go through 3 different
machines
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