There are n different books and p copies of each in a library. Find the number of ways in which one or more than one books can be selected.

Answer

To find the number of ways to select one or more books from a library containing \( n \) different books, each with \( p \) copies, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Selection Process**:
Each book can be selected in several ways:
- You can choose not to select any copy of the book (0 copies).
- You can select 1 copy of the book.
- You can select 2 copies of the book.
- ...
- You can select up to \( p \) copies of the book.

Thus, for each book, the number of ways to select copies is \( p + 1 \) (including the option of selecting 0 copies).

2. **Calculating Total Selections for All Books**:
Since there are \( n \) different books and the selection of each book is independent of the others, the total number of ways to select books (including the option of selecting none) is:
\[ (p + 1)^n \]
This accounts for all combinations of selections across all \( n \) books.

3. **Excluding the Case of Selecting No Books**:
The above calculation includes the scenario where none of the books are selected (i.e., selecting 0 copies of each book). Since we want to find the number of ways to select **one or more** books, we need to subtract this one case from our total:
\[ \text{Total selections of one or more books} = (p + 1)^n - 1 \]

### Final Answer:
Thus, the number of ways in which one or more than one book can be selected is:
\[ (p + 1)^n - 1 \]