The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is

Options

A. `2^(n)-2`
B. `2^(n)-1`
C. `2^(n-1)-1`
D. `2^(n)-1`

Explanation

To solve the problem of finding the number of ways to put \( n \) distinct objects into two identical boxes such that no box remains empty, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have \( n \) distinct objects and we want to distribute them into two identical boxes (let's call them Box A and Box B) such that neither box is empty.

2. **Total Distributions Without Restrictions**: If the boxes were distinct (i.e., if we could tell Box A from Box B), each object can go into either Box A or Box B. Therefore, for \( n \) objects, the total number of ways to distribute them would be \( 2^n \).

...