In how many ways can 5 distinct books be arranged on a shelf such that two specific mathematics books are always placed next to each other?
Answer and explanation
Correct answer: D. 48 ways
- Step 1: Tie the two specific mathematics books together as a single block: [M1 M2].
- Step 2: Now we have 4 units to arrange: the block and the other 3 books.
- Step 3: Number of ways to arrange 4 units: 4! = 24 ways.
- Step 4: The two mathematics books within the block can be arranged in 2! = 2 ways (M1 M2 or M2 M1).
- Step 5: Total arrangements: 4! 2! = 24 2 = 48 ways.
Answer
48 ways.
Why not the others: '24 ways' forgets that the two books inside the block can swap positions; '120 ways' is 5! (arranging without any constraint); '12 ways' divides by 2.
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