What is the number of arrangements of 5 distinct books on a shelf if 2 particular books must always be adjacent?

Answer and explanation

Correct answer: D. 48

  1. Step 1: Tie the 2 particular books together as a single block. Now we have 4 units to arrange.
  2. Step 2: Number of ways to arrange 4 units is .
  3. Step 3: The 2 particular books can be arranged internally in ways.
  4. Step 4: Total arrangements: .
Answer
48.
Why not the others: '24' forgets that the 2 books can swap places (); '36' is an arbitrary product; '120' is total unrestricted arrangements ().

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