Statement-1: A student is allowed to select at most n books from a collection of (2n+1) books. If the total number of ways in which he can select at least one book is 255, then n=3.
Statement-2 `sum_(r=1)^(n)""^(2n+1)C_(r)=2^(2n)`

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem step by step, let's break down the statements and calculations involved.

### Step 1: Understanding the Problem
We need to determine if the statements about selecting books from a collection are true. The student can select at most \( n \) books from a total of \( 2n + 1 \) books, and the total number of ways to select at least one book is given as 255.

### Step 2: Total Ways to Select Books
The total number of ways to select any number of books from \( 2n + 1 \) books is given by the formula:
\[
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