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

Answer

To solve the problem of selecting at least one book from a shelf of 12 different books, we can follow these steps:

### Step 1: Understand the Problem
We need to find the number of ways to select at least one book from a total of 12 different books. The phrase "at least one" means we can select one, two, three, and so on, up to all 12 books.

### Step 2: Calculate Total Selections
For each book, we have two choices: either to select it or not to select it. Therefore, for 12 books, the total number of ways to choose any combination of books (including the option of not choosing any books) is given by \(2^{12}\).

### Step 3: Exclude the Case of Selecting No Books
Since we need to select at least one book, we must subtract the case where no books are selected. The number of ways to select no books is 1 (the empty set).

### Step 4: Final Calculation
Thus, the total number of ways to select at least one book is:
\[ 2^{12} - 1 \]

### Step 5: Compute the Value
Calculating \(2^{12}\):
\[ 2^{12} = 4096 \]
Now, subtracting 1 gives:
\[ 4096 - 1 = 4095 \]

### Conclusion
The total number of ways to select at least one book from 12 different books is **4095**.

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