Question

In a sheet metal operation, three identical notches and four identical bends are required. If the operations can be done in any order, how many different possible sequences are there to complete the manufacturing?

Answer 1

Answer:

There are 5040 different possible sequences.

Step-by-step explanation:

Three identical notches and four identical bends are required in the sheet metal operation.

In total 7 things are required in the metal operation.

We can think it as we need to put the 3 notches and 4 bends in 7 places.

First, lets put the 3 notches in 3 places.

In order to do so, we need to choose 3 places from the 7 places.

We can choose 3 places in $\frac{7!}{3!\times4!} = \frac{5\times6\times7}{6} = 35$ ways.

The 3 notches can be arrange in 3! = 6 ways.

The 4 bends can arrange in 4! = 24 ways.

Thus, in total $35\times24\times6 = 5040$ different possible sequences.