How many different arrangements of distinct books are possible on a shelf?

Answer and explanation

Correct answer: C. 5040

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  1. Step 1: The number of distinct linear permutations of distinct objects on a shelf is given by .
  2. Step 2: Apply the factorial for : .
  3. Step 3: Multiplying out the factors gives different book arrangements.
Answer
5040.
Why not the others: '720' calculates , which is the formula for circular arrangements rather than a linear shelf; '42' calculates , permuting only of the books; '49' calculates , incorrectly assuming independent replacement choices without decrementing.

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