There are three stations A, B and C and five routes for going from station A to B and four routes from station B to C. Find the number of different ways through which a person can go from A to C via B.

Answer

To solve the problem of finding the number of different ways a person can go from station A to station C via station B, we can break down the solution into clear steps.

### Step-by-Step Solution:

1. **Identify the Routes from A to B**:
- There are 5 different routes available for traveling from station A to station B.

2. **Identify the Routes from B to C**:
- There are 4 different routes available for traveling from station B to station C.

3. **Calculate the Total Ways from A to C via B**:
- To find the total number of different ways to travel from A to C via B, we multiply the number of routes from A to B by the number of routes from B to C.
- This can be expressed mathematically as:
\[ \text{Total Ways} = (\text{Ways from A to B}) \times (\text{Ways from B to C}) = 5 \times 4 \]

4. **Perform the Multiplication**:
- Calculate \(5 \times 4\):
\[ 5 \times 4 = 20 \]

5. **Conclusion**:
- Therefore, the total number of different ways a person can go from station A to station C via station B is **20**.

### Final Answer:
The number of different ways through which a person can go from A to C via B is **20**.

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