Question

A part is labeled by printing with four thick lines, three medium lines, and two thin lines. If each ordering of the nine lines represent a different label, how many different labels can be generated by using this scheme?

Answer 1

By using the formula, we determine there are 1260 different labels possible with the given scheme of four thick, three medium, and two thin lines.

Step-by-step explanation:

The question asks for the number of different labels that can be generated with four thick lines, three medium lines, and two thin lines, assuming each arrangement represents a unique label. This is a combinatorics problem which involves calculating permutations of items with repetitions.

To solve this, we use the formula for permutations of multiset items. This equation takes into account the total number of items (9 lines in total) and the repetitions among them (4 thick, 3 medium, and 2 thin lines). The factorial notation (e.g., 4!) signifies the product of all positive integers up to that number. Therefore, there are 1260 different labels possible with the given scheme.