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.
the same route is taken

Answer

To solve the problem, we need to determine the total number of different ways a man can travel from station A to station B and then return to station A, given that there are five routes available for the journey.

### Step-by-Step Solution:

1. **Identify Routes for Going from A to B**:
- The man has 5 different routes to choose from when traveling from station A to station B.

2. **Identify Routes for Returning from B to A**:
- Since the problem states that the same route is taken for returning, the man will also use the same route he took to go from A to B. This means he has 1 choice for the return journey based on the route he selected initially.

3. **Calculate Total Ways**:
- For each of the 5 routes taken to go from A to B, there is exactly 1 corresponding route for returning back to A. Therefore, the total number of different ways to complete the journey (going to B and returning to A) can be calculated as follows:
\[ \text{Total Ways} = (\text{Number of ways to go}) \times (\text{Number of ways to return}) = 5 \times 1 = 5 \]

4. **Final Result**:
- The total number of different ways the man can go from A to B and return to A is 5.