Non-Adjacent Books

Count total arrangements and subtract those where the two books are adjacent.

Treat the two adjacent books as a single block to count the bad arrangements.

1. 1. Total arrangements

   There are $5!=120$ total arrangements of 5 distinct books.

2. 2. Adjacent arrangements

   Treat the two restricted books as a block: $4!\times 2=48$ arrangements have them adjacent.

3. 3. Subtract

   Valid arrangements: $120-48=72$.

   $$120-48=72$$

Answer: 72