A shopkeeper has 11 copies each of nine different books, then the number of ways in which atleast one book can be selected is

Options

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

Answer

To solve the problem of how many ways at least one book can be selected from 11 copies each of 9 different books, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Choices**:
Each of the 9 books has 11 copies. For each book, the shopkeeper can choose to take anywhere from 0 to 11 copies. This means for each book, there are 12 possible choices (0, 1, 2, ..., 11).

2. **Calculating Total Choices**:
Since there are 9 different books, and for each book, there are 12 choices, the total number of ways to choose books (including the option of not choosing any books) is given by:
\[ \text{Total Choices} = 12^9 \]

3. **Excluding the Case of Choosing No Books**:
The problem asks for the number of ways to select at least one book. The only case we need to exclude is the scenario where no books are selected at all (which is just 1 way). Therefore, we subtract this case from our total choices:
\[ \text{Ways to select at least one book} = 12^9 - 1 \]

4. **Calculating the Final Answer**:
Now we compute \(12^9\):
\[ 12^9 = 51520374361 \]
Thus, the number of ways to select at least one book is:
\[ 51520374361 - 1 = 51520374360 \]

### Final Answer:
The number of ways in which at least one book can be selected is \(51520374360\).