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Chapter 5: Problem 378

A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, than number of ways in which the car can be filled is (a) 10 (b) 20 (c) 30 (d) 40

Short Answer

Expert verified
The total number of ways to fill the car is \[2*5*4=40\] ways. Therefore, the correct answer is (d) 40.

Step by step solution

01

Calculate driver combinations

Since there are 2 drivers among the 6 persons, we can calculate the combinations for placing a driver in the driver's seat. Since we only need 1 driver, there are two (2) ways to choose a driver.
02

Calculate combinations for front passenger seat

Now that we have chosen one driver in step 1, we are left with 5 persons (1 driver and 4 non-drivers) to choose from for the front passenger seat. We have 5 choices for the front passenger seat.
03

Calculate combinations for rear seat

Once the driver and front passenger have been chosen, we are left with 4 persons to choose from for the rear seat (since there are 6 persons in total and 2 are already seated). So we have 4 choices for the rear seat.
04

Calculate the total number of ways to fill the car

Now we need to find the total number of ways to fill the car based on the number of combinations in each step. We multiply the combinations in each step to find the result. Total ways = (Driver combinations) * (Front passenger combinations) * (Rear seat combinations) Total ways = 2 * 5 * 4
05

Find the answer

After performing the calculation, we find that there are \[2*5*4=40\] ways in which the car can be filled. Therefore, the correct answer is (d) 40.

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