There are 10 buses running between Delhi and Agra. In how many ways can a man go from Delhi to Agra and return by a different bus?

Answer

To solve the problem of how many ways a man can go from Delhi to Agra and return by a different bus, we can break it down into the following steps:

### Step 1: Determine the number of buses available
There are 10 buses running from Delhi to Agra. This means that when the man is leaving Delhi, he has 10 options to choose from.

### Step 2: Choose a bus to go from Delhi to Agra
The man can choose any one of the 10 buses to travel from Delhi to Agra. Therefore, the number of ways to choose a bus for the journey from Delhi to Agra is:
- **Number of ways to choose a bus = 10**

### Step 3: Determine the options for returning
When the man wants to return from Agra to Delhi, he must take a different bus than the one he took to go to Agra. Since he has already used one bus, there are 9 buses left for him to choose from for the return journey.

### Step 4: Choose a bus to return from Agra to Delhi
The man can now choose any one of the remaining 9 buses to return to Delhi. Therefore, the number of ways to choose a bus for the return journey is:
- **Number of ways to choose a return bus = 9**

### Step 5: Calculate the total number of ways
To find the total number of ways the man can go from Delhi to Agra and return by a different bus, we multiply the number of ways to go with the number of ways to return:
- **Total number of ways = Number of ways to go × Number of ways to return**
- **Total number of ways = 10 × 9 = 90**

Thus, the total number of ways the man can travel from Delhi to Agra and return by a different bus is **90**.