Question

a manufacturing operation consists of 10 operations; 5 of them are distinct machining operations and the other 5 are distinct assembly operations. however, five machining operations must be completed before any of the five assembly operations can begin. within each set of five, operations can be completed in any order. how many different production sequences are possible?

Answer 1

14,400 production sequences are possible.

Since the first set of machining operations can be performed in any order, after selecting one, there are 4 operations left. After selecting another, there are 3 operations left.

After selecting yet another, there are 2 operations left. Finally, after selecting yet another, there is only 1 operation left. This procedure may be described by the equation below: There are 120 potential options when multiplying 5 by 4 by 3 by 2 by 1. It may also be written mathematically as 5! = 120.

Here, We have 5 × 4 x 3 x 2 x 1 = 120 potential unique options for the final five assembly processes.

So total number of combinations will be - 120 × 120

= 14,400

To learn more about Combinations from given link

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