There are 6 trains running between Indore and Bhopal . In how many ways can a man go from Indore to Bhopal and return by a different train ?

Answer

To solve the problem of how many ways a man can go from Indore to Bhopal and return by a different train, we can break it down into steps:

### Step-by-Step Solution:

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

2. **Choose a train for the journey from Indore to Bhopal**:
The man can choose any of the 6 trains to go from Indore to Bhopal.
- **Ways to go**: 6 ways

3. **Choose a different train for the return journey**:
Since the man must return by a different train, he cannot use the same train he took to go to Bhopal. Therefore, he has 5 remaining trains to choose from for his return journey.
- **Ways to return**: 5 ways

4. **Calculate the total number of ways**:
To find the total number of ways he can make the round trip, we multiply the number of ways to go by the number of ways to return.
- Total ways = Ways to go × Ways to return
- Total ways = 6 × 5 = 30

### Final Answer:
The man can go from Indore to Bhopal and return by a different train in **30 ways**.

---