Kelly has different books to arrange on a​ shelf; 4 ​blue, 2 ​green, and 3red. Answer parts a through e below. ​(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.

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.