There are 6 trains running between indore and Bhopal ., if the person can return by any one of the 6 trains , then find the number of ways in which he can go from indore to bhopal and return from bhopal to indore .

Answer

To solve the problem, we need to determine the number of ways a person can travel from Indore to Bhopal and then return from Bhopal to Indore using the available trains.

### Step-by-Step Solution:

1. **Identify the number of trains available:**
There are 6 trains running between Indore and Bhopal.

2. **Determine the number of ways to go from Indore to Bhopal:**
Since there are 6 trains, the person has 6 different options to travel from Indore to Bhopal.

3. **Determine the number of ways to return from Bhopal to Indore:**
Similarly, for the return journey from Bhopal to Indore, the person can also choose from any of the 6 trains. Thus, there are 6 options for the return trip as well.

4. **Calculate the total number of ways to complete the round trip:**
To find the total number of ways to go from Indore to Bhopal and then return, we multiply the number of ways to go by the number of ways to return:
\[ \text{Total ways} = (\text{Ways to go}) \times (\text{Ways to return}) = 6 \times 6 = 36 \]

5. **Conclusion:**
Therefore, the total number of ways in which the person can go from Indore to Bhopal and return is **36**.