. The store sells bracelets with 12 slots for gems to be added (in a line, not a circle), and she buys 4 rubies, 4 emeralds, 3 sapphires and 1 diamond to put in the bracelet. Gems of the same type are indistinguishable. a) [1] How many ways different ways are there to arrange the 12 gems? b) [2] How many different ways are there to arrange the gems such that no two emeralds are next to each other? c) [2] How many different ways are there to arrange the gems such that each ruby is next to at least one other ruby?