How many different arrangements of distinct books are possible on a shelf?
Answer and explanation
Correct answer: D. 120
**
- Step 1: The number of distinct linear permutations of distinct objects on a shelf is given by .
- Step 2: Apply the factorial for : .
- Step 3: Multiplying out the factors gives different book arrangements.
Answer
120.
Why not the others: '25' calculates , incorrectly assuming independent replacement choices without decrementing; '20' calculates , permuting only of the books; '24' calculates , which is the formula for circular arrangements rather than a linear shelf.
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