There are 12 different books in a shelf. In how many ways we can select atleast one of them?

Answer

To find the number of ways to select at least one book from a shelf of 12 different books, we can use the principle of combinations and the concept of the power set.

### Step-by-step Solution:

1. **Understanding the Total Selections**:
Each book can either be selected or not selected. Therefore, for each of the 12 books, there are 2 choices (select or not select).

2. **Calculating Total Combinations**:
Since there are 12 books, the total number of ways to select any combination of these books (including selecting none) is given by \(2^{12}\). This is because for each book, you have 2 options (to include it or not).

\[ \text{Total combinations} = 2^{12} \]

3. **Excluding the Empty Selection**:
The total combinations calculated above includes the case where no books are selected (the empty set). Since we want at least one book, we need to subtract this one case from the total.

\[ \text{Combinations with at least one book} = 2^{12} - 1 \]

4. **Calculating \(2^{12}\)**:
We calculate \(2^{12}\):
\[ 2^{12} = 4096 \]

5. **Final Calculation**:
Now, subtracting the empty selection:
\[ 2^{12} - 1 = 4096 - 1 = 4095 \]

Thus, the total number of ways to select at least one book from 12 different books is **4095**.