What is the total number of ways of selecting atleast one object from 2 sets of 12 different objects each set contains 6 objects ?

Options

A. 4096
B. 4095
C. 2048
D. none of these

Answer

To solve the problem of selecting at least one object from two sets of 12 different objects (each set containing 6 objects), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two sets, each containing 6 different objects, making a total of 12 different objects. We need to find the total number of ways to select at least one object from these sets.

2. **Total Number of Objects**:
Since we are considering both sets together, we treat them as a single set of 12 different objects: O1, O2, O3, O4, O5, O6, O7, O8, O9, O10, O11, O12.

3. **Calculating Total Selections**:
The total number of ways to select objects from a set of n objects is given by \(2^n\). This includes all possible selections, including the empty selection (selecting no objects).

For our case with 12 objects:
\[ \text{Total selections} = 2^{12} = 4096 \]

4. **Excluding the Empty Selection**:
Since we need to select at least one object, we must exclude the empty selection from our total. Therefore, we subtract 1 from the total selections:
\[ \text{Selections with at least one object} = 4096 - 1 = 4095 \]

5. **Final Answer**:
The total number of ways to select at least one object from the two sets of 12 different objects is:
\[ \boxed{4095} \]