A manufacturing operation consists of 10 operations. However, five machining operations must be completed before any of the remaining five assembly operations can begin. Within each set of five, operations can be completed in any order. How many different production sequences are possible?

The answer is: 14,400 different production sequences are possible

Explanation:

For this calculation I will assume that the first 5 operations can be made in any order, as well as the last 5.

For the first set of machining operations, since they can go in any order, you choose one operation and then you have 4 operations left, then you choose another operation and you have 3 operations left, then you choose another operation and you have 2 operations left, you choose another option and you have only 1 operation left. This process can be expressed by the following equation: 5 x 4 x 3 x 2 x 1 = 120 possible different combinations. Mathematically it can also be expressed as 5! = 120

The same for the last 5 assembly operations, you have 5 x 4 x 3 x 2 x 1 = 120 possible different combinations.

So to get the total possible combinations of all the process, we just multiply 120 x 120 = 14,000 or 5! x 5! = 14,400