Ten books are randomly arranged on a shelf. What is the probability that a specific pair of books will be positioned side by side?

Explanation

There are 10! possible ways to arrange the 10 books. Treating the chosen pair as a single unit, we have 9! arrangements for the combined unit and the remaining books. Since the two books in the pair can be swapped, multiply by 2!. Therefore, the total favorable arrangements are 9! × 2!. The probability is (9! × 2!) / 10! = 1/5.