Four buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, find the total possible ways.

Explanation

To solve the problem of how many ways a man can travel from Gwalior to Bhopal and back using different buses, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Identify the Buses**:
There are 4 buses running between Gwalior and Bhopal. Let's label them as Bus A, Bus B, Bus C, and Bus D.

2. **Choosing the Outbound Bus**:
When the man travels from Gwalior to Bhopal, he can choose any one of the 4 buses. Therefore, the number of ways to choose the outbound bus is:
\[ \text{Ways to choose outbound bus} = 4 \]

3. **Choosing the Return Bus**:
For the return journey, the man must take a different bus than the one he used to go to Bhopal. Since he has already used one bus, he has 3 remaining buses to choose from. Therefore, the number of ways to choose the return bus is:
\[ \text{Ways to choose return bus} = 3 \]

4. **Calculating Total Ways**:
To find the total number of ways the man can travel to Bhopal and back, we multiply the number of choices for the outbound bus by the number of choices for the return bus:
\[ \text{Total ways} = (\text{Ways to choose outbound bus}) \times (\text{Ways to choose return bus}) = 4 \times 3 = 12 \]

5. **Final Answer**:
Therefore, the total number of possible ways for the man to travel from Gwalior to Bhopal and back using different buses is:
\[ \text{Total possible ways} = 12 \]