A construction worker is building a straight walking path that is 5m long from a client's front door to the sidewalk. The path is to be built out of planks that are 60 cm, 70cm, and 100 cm in length. How many different paths could be constructed using these plank lengths?
Details and assumptions
2 paths are different if the planks used are not in the same order. For example, the path constructing using planks \( 100, 70, 60, 70, 100\) is different from the path constructed using planks \(100, 100, 70, 60, 70\).
The worker has enough quantities of each different length of planks.