A shopkeeper has 10 copies of each of nine different books, then number of ways in which atleast one book can be selected is

Options

A. A) `9^(11)-1`
B. B) `10^(10)-1`
C. C) `11^(9)-1`
D. D) `10^9`

Answer

To solve the problem of finding the number of ways in which at least one book can be selected from a shopkeeper who has 10 copies of each of nine different books, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Books**:
The shopkeeper has 9 different books.

2. **Determine the Copies of Each Book**:
Each book has 10 copies available.

3. **Calculate the Number of Ways to Select Each Book**:
For each book, you can select:
- 0 copies (not selecting the book)
- 1 copy
- 2 copies
- ...
- 10 copies

Therefore, for each book, the number of ways to select is:
\[ 0 + 1 + 2 + ... + 10 = 11 \text{ ways} \]
(including the option of not selecting the book).

4. **Calculate the Total Number of Ways to Select Books**:
Since there are 9 books and each book can be selected in 11 different ways, the total number of ways to select books is:
\[ 11^9 \]

5. **Subtract the Case of Selecting No Books**:
The total calculated above includes the scenario where no books are selected (which is 1 way). To find the number of ways to select at least one book, we need to subtract this case:
\[ \text{Total ways to select at least one book} = 11^9 - 1 \]

6. **Final Calculation**:
The final answer is:
\[ 11^9 - 1 \]