Two persons go in a railways carriage where there are 6 vacant seats. In how many different ways can they seat themselves?

Answer

To solve the problem of how many different ways two persons can seat themselves in a railway carriage with 6 vacant seats, we can follow these steps:

### Step-by-step Solution:

1. **Identify the number of seats available**: There are 6 vacant seats in the railway carriage.

2. **Choose a seat for the first person**: The first person can choose any of the 6 seats available. Therefore, there are 6 options for the first person.

\[ \text{Choices for Person 1} = 6 \]

3. **Choose a seat for the second person**: After the first person has taken a seat, there will be 5 seats remaining for the second person. Thus, there are 5 options for the second person.

\[ \text{Choices for Person 2} = 5 \]

4. **Calculate the total number of arrangements**: To find the total number of ways both persons can seat themselves, we multiply the number of choices for the first person by the number of choices for the second person.

\[ \text{Total arrangements} = \text{Choices for Person 1} \times \text{Choices for Person 2} = 6 \times 5 = 30 \]

5. **Conclusion**: Therefore, the total number of different ways in which the two persons can seat themselves is 30.

### Final Answer:
The total number of ways in which the two persons can seat themselves is **30**.

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