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 the given conditions, we can break it down step by step.

### Step 1: Identify the roles in the car
The car has:
- 1 driver in the front seat
- 1 passenger in the front seat
- 1 passenger in the rear seat

### Step 2: Determine the number of drivers
Out of the 6 persons, 2 can drive. Therefore, we need to select 1 driver from these 2.

**Calculation:**
The number of ways to choose 1 driver from 2 is given by the combination formula:
\[ \text{Ways to choose a driver} = \binom{2}{1} = 2 \]

### Step 3: Select a passenger for the front seat
After selecting the driver, there are now 5 persons left (1 driver and 4 non-drivers). We can choose any of these 5 persons to sit in the front passenger seat.

**Calculation:**
The number of ways to choose 1 front passenger from 5 is:
\[ \text{Ways to choose a front passenger} = 5 \]

### Step 4: Select a passenger for the rear seat
After filling the front seats, there are now 4 persons left (1 driver and 3 non-drivers). We can choose any of these 4 persons to sit in the rear seat.

**Calculation:**
The number of ways to choose 1 rear passenger from 4 is:
\[ \text{Ways to choose a rear passenger} = 4 \]

### Step 5: Calculate the total number of ways
Now, we can multiply the number of ways to choose each position:
\[ \text{Total ways} = \text{Ways to choose a driver} \times \text{Ways to choose a front passenger} \times \text{Ways to choose a rear passenger} \]
\[ \text{Total ways} = 2 \times 5 \times 4 = 40 \]

Thus, the total number of ways in which the car can be filled is **40**.

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

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