At a college library exhibition of faculty publications, three mathematics books, three social science books, and two biology books will be displayed on a shelf. (Assume that all of the books are different.) (a) In how many ways can the eight books be arranged on the shelf?  ways (b) In how many ways can the eight books be arranged on the shelf if books on the same subject matter are placed 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.