Assignment:
Wing has different books to arrange on a shelf: 4 blue, 3 green, and 2 red.
(a) In how many ways can the books be arranged on a shelf?
(b) If books of the same color are to be grouped together, how many arrangements are possible?
(c) In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together?
(d) In how many ways can you select 3 books, one of each color, if the order in which the books are selected does not matter?
Provide complete and step by step solution for the question and show calculations and use formulas.