A 9-volume numbered set of books is placed randomly on a shelf. What is the probability that the books will be numbered in the correct order from left to right? The probability is \( \square \). (Type a simplified fraction.)

To find the probability that the 9-volume numbered set of books is in the correct order from left to right, we first recognize that there are \( 9! \) (factorial of 9) different ways to arrange the 9 books. This is because each of the 9 books can occupy any position on the shelf without any restrictions. Out of these \( 9! \) arrangements, only 1 arrangement is the correct order (i.e., the order from 1 to 9). Thus, the probability \( P \) that the books are in the correct order is given by: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{9!} \] Calculating \( 9! \): \[ 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362880 \] Therefore, the probability that the books are in the correct order is: \[ P = \frac{1}{362880} \] So, the final answer is: The probability is \( \frac{1}{362880} \).