Question #47092

True or false. Give reason.

The total number of possible sequences for processing 5 jobs on 4 machines is 5^4.
1

Expert's answer

2014-10-02T09:27:01-0400

Answer on Question #47092 – Math – Combinatorics | Number Theory

True or false. Give reason.

The total number of possible sequences for processing 5 jobs on 4 machines is 545^{4}.

Solution

False.

Suppose machines admit simultaneous processing different jobs. The total number of possible sequences for processing 5 jobs on 1 machine is 5! Thus the total number of possible sequences for processing 5 jobs on 4 machines is (5!)4≠54(5!)^{4} \neq 5^{4}.

Suppose we can choose only one job out of 5 to process on one machine. The total number of possible sequences for processing 5 jobs on 1 machine is 5. Thus the total number of possible sequences for processing 5 jobs on 4 machines is 545^{4}.

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