The marketing department has been given the assignment of designing colour codes for the 42 different lines of compact disks (CDs) sold by Goody Records. Three colours are to be used on each CD, but a combination of three colours used for one CD cannot be rearranged and used to identify a different CD. This means that if green, yellow, and violet were used to identify one line, then yellow, green, and violet (or any other combination of these three colours) cannot be used to identify another line.
a. Would seven colours taken three at a time be adequate to colour code the 42 lines?
b. As an alternative plan for colour coding the 42 different lines, it has been suggested that only two colours be placed on a disk. Would 10 colours be adequate to colour code the 42 different lines? (Again, a combination of two colours could be used only once).