A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, then the number of ways in which the car can be filled is:

Options

A. 10
B. 40
C. 30
D. 20

Answer

To solve the problem of how many ways the car can be filled with 2 people in the front seat (1 of whom must be a driver) and 1 person in the rear seat from a group of 6 people (of which 2 can drive), we can break it down into steps.

### Step-by-Step Solution:

1. **Identify the Drivers**:
- There are 6 persons in total, and out of these, 2 can drive.

2. **Choose the Driver**:
- Since only one driver can occupy the driver's seat, we can choose 1 driver from the 2 available drivers.
- The number of ways to choose 1 driver from 2 is given by the combination formula \( C(2, 1) \):
\[ C(2, 1) = 2 \]
- So, there are 2 ways to choose the driver.

3. **Remaining Persons**:
- After selecting the driver, we have 5 persons left (6 total - 1 driver = 5 remaining).

4. **Choose the Front Seat Passenger**:
- The front seat now has 1 more space available (besides the driver), and we can fill this seat with any of the remaining 5 persons.
- Therefore, we have 5 choices for the front seat passenger.

5. **Choose the Rear Seat Passenger**:
- After filling the front seat, we have 4 persons left (5 remaining - 1 front seat passenger = 4 remaining).
- We can choose 1 person from these 4 to sit in the rear seat.
- So, we have 4 choices for the rear seat passenger.

6. **Calculate Total Arrangements**:
- The total number of ways to fill the car can be calculated by multiplying the number of ways to choose the driver, the front seat passenger, and the rear seat passenger:
\[ \text{Total Ways} = (\text{Ways to choose driver}) \times (\text{Ways to choose front seat}) \times (\text{Ways to choose rear seat}) \]
\[ \text{Total Ways} = 2 \times 5 \times 4 = 40 \]

### Final Answer:
The total number of ways in which the car can be filled is **40**.

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