What are the number of ways of arranging 9 books out of 14 in a library where the librarian, while arranging the books, got 2 damaged books and sent them for rebinding and repairing?

To solve this problem, we need to determine the number of ways to arrange 9 books out of 14 in a library, considering that 2 of the 14 books are damaged and sent for rebinding. Here's how to approach it:

### Step 1: Determine the number of usable books
Initially, there are 14 books, but since 2 are damaged, only \(14 - 2 = 12\) books are available for arranging.

### Step 2: Calculate the number of ways to select 9 books from 12
We need to choose 9 books from the 12 available books. The number of ways to do this is given by the combination formula:
\[
\text{Number of ways to choose 9 books from 12} = \binom{12}{9}
\]
\[
\binom{12}{9} = \frac{12!}{9! \cd

Calculate the number of ways to arrange 9 books out of 14 in a library, considering that 2 books are damaged and sent for rebinding. Understand the combinatorial concept of combinations and permutations with a detailed solution. Suitable for advanced high school students.

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