To lower manufacturing costs at an engineering company, they are trying to design printed circuit boards (PCBs) that can be reused on a number of products. For some products, not all components will be assembled on the board. For some products, all components will be assembled. After some study, a first PCB comes out and it has 8 sockets for a common chip. So up to 8 of these chips can be assembled. For the lower model of the product this will have 5 chips assembled and for the upper model, all 8 sockets will be populated.
a) How many different ways can they assemble the 5 chips on the 8 empty sockets?
b) Suppose they start production of a medical version of the same product. The medical model is based on the upper model, where all 8 sockets are filled. But now, on 4 of the sockets high-grade,
high-quality chips are assembled, and on the remaining 4 low-grade commercial chips are assembled. How many different ways can they assemble the 8 chips now?