AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 6 Medium

There are 9 different books: 3 math books, 4 Chinese books, and 2 English books. These books are to be arranged in a row on a shelf, with the math books kept together and the Chinese books kept together. Then there are            possible arrangements in total.

Answer:3456

Since the books of the same subject must be placed together, we can “bundle” them. First, bundle the math books and the Chinese books, making two bundles. Together with the two English books, we have four items to arrange. After arranging these, we then order the books within each bundle.

Therefore, the total number of arrangements is _{4}P_{4} \times _{4}P_{4} \times _{3}P_{3} = 3456 \quad (\text{ways}).

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