There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning.
any of the routes is taken

Answer

To solve the problem of how many different ways a man can go from station A to B and return, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the number of routes available**:
There are 5 different routes from station A to station B.

2. **Determine the number of ways to go from A to B**:
Since there are 5 routes, the number of ways to go from A to B is 5.

3. **Determine the number of ways to return from B to A**:
Similarly, there are also 5 routes available for returning from B to A. Therefore, the number of ways to return is also 5.

4. **Calculate the total number of ways for the round trip**:
Since the journey to B and the return journey from B to A are independent events, we can multiply the number of ways to go and the number of ways to return.
\[ \text{Total ways} = (\text{Ways from A to B}) \times (\text{Ways from B to A}) = 5 \times 5 = 25 \]

5. **Conclusion**:
Therefore, the total number of different ways a man can go from A to B and return is 25.

### Final Answer:
The total number of different ways to go from A to B and return is **25**.

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