Discussion
In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
Answer: B
Count all orders, then remove those with A and B together.
\[ \text{total} = 4! = 24 \]
Treating A and B as one block gives three units, and the pair can be either way round:
\[ 3! \times 2! = 6 \times 2 = 12 \]
\[ 24 - 12 = 12 \]
With only four books, exactly half the arrangements keep A and B apart.
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