Question

Six people out of whom only two can drive are to be seated in a six seater car with two seats in front and four in the rear. The people who know driving don’t sit together. Only someone who knows driving can sit on the driver’s seat. Evaluate the number of ways the six people can be seated.

Answer 1

Answer:

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Answer 2

Answer:

In 192 ways six people can be seated in a six-seater car.

Step-by-step explanation:

Points to remember while solving the question:

• There are 6 people in total
• Only 2 people know how to drive
• The person who knows driving cannot sit together
• Only someone who knows driving can sit in the driver’s seat

To find,

The number of ways the six people can be seated.

Calculation,

Step(1): As there are 2 people who can sit in the driver's seat, so the number of possibilities for the driver's seat is TWO.

Step(2): As the person who knows driving cannot sit together, the seat in the front of the car must be occupied by the remaining 4 people who don't know driving. And that can be done in 4C1 ways = FOUR.

Step(3): Now, the remaining people can occupy the back seats of the car in 4 × 3 × 2 × 1 ways = 24. Because we will let one person sit in any one back seat, then for remaining 3 people, and for 2 people.

Hence, the total number of ways is 2 × 4 × 24 = 192 ways.

Therefore, in 192 ways six people can be seated in a six-seater car.

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