Could someone please explain how to do this problem?

Question

Assume that there are 6 types of upholstery, 2 types of wood, and 5 designs to choose from. Of the designs, 4 designs permit both a choice of wood and a choice of upholstery, but 1 of the design allows only a choice of upholstery.

How many different chairs can be made?

Answer 1

If the choices for upholstery, wood and design can be made separately, the answer would be the product of the number of choices for each =

6 x 2 x 5 = 60

This is true for 4 of the designs, but not for the 5th one. The 5th design only allows a choice for upholstery. This 5th design only has 6 chairs as possible choices.

So the number of chairs that can be made is the 6 chairs for the 5th design added to 6 x 2 x 4 = 48 for the other 4 designs = 54.