A shelf holds 12 books in a row. How many ways are there

Chapter 9, Problem 46E

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Problem 46E

A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen? [Hint: Represent the books that are chosen by bars and the books not chosen by stars. Count the number of sequences of five bars and seven stars so that no two bars are adjacent.]

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