Question
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.)
Ask by Davison Sanders. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability is \(\frac{1}{362880}\).
Solution
The probability of the books being in the correct order is:
\[
\frac{1}{362880}
\]
This is because there are \(9!\) (362,880) possible ways to arrange the 9 books, and only one of those arrangements is the correct order.
\boxed{\dfrac{1}{362880}}
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Simplify this solution Bonus Knowledge
To find the probability that the 9-volume numbered set of books is arranged in the correct order from left to right, we can start by determining the total number of ways to arrange the 9 books. The total arrangements is given by \(9!\) (9 factorial), which equals \(362880\). Since there is only one correct order among these arrangements (the books in the order from 1 to 9), the probability \(P\) is calculated as: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{9!} = \frac{1}{362880}. \] So the probability that the books will be numbered correctly from left to right is \( \frac{1}{362880} \).
