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 books is 63 find the value of n.

Explanation

To solve the problem step by step, we will analyze the situation where a student can select at most \( n \) books from a collection of \( 2n + 1 \) books, and the total number of ways to select these books is given as 63.

### Step 1: Understand the total number of selections
The total number of ways to select books from \( 2n + 1 \) books, selecting at most \( n \) books, can be expressed mathematically. The total number of ways to select \( k \) books from \( 2n + 1 \) books is given by the binomial coefficient \( \binom{2n+1}{k} \).

### Step 2: Write the expression for total selections
The total number of ways to select at most \( n \) books is:
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