There are 15 buses running between Lucknow and Kanpur. In how many ways can a man go to Kanpur and return by a different bus?

Options

A. 280
B. 310
C. 240
D. 210

Answer

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

### Step-by-Step Solution:

1. **Identify the number of buses**:
There are 15 buses running between Lucknow and Kanpur.

2. **Choose a bus for the onward journey**:
The man can choose any one of the 15 buses to go from Lucknow to Kanpur. So, there are 15 options for the first leg of the journey.

\[ \text{Ways to choose a bus to Kanpur} = 15 \]

3. **Choose a different bus for the return journey**:
Since the man must return by a different bus, after choosing one bus for the onward journey, he has 14 remaining buses to choose from for the return journey.

\[ \text{Ways to choose a different bus to return} = 14 \]

4. **Calculate the total number of ways**:
To find the total number of ways to go to Kanpur and return by a different bus, we multiply the number of choices for the onward journey by the number of choices for the return journey.

\[ \text{Total ways} = \text{Ways to Kanpur} \times \text{Ways to return} = 15 \times 14 \]

\[ \text{Total ways} = 210 \]

Thus, the total number of ways the man can go to Kanpur and return by a different bus is **210**.