differentiate linear and circular permutation

 Which of the following scenarios best illustrates a linear permutation?

• Arranging beads in a circular necklace.

• Arranging books on a shelf.

• Arranging chairs around a circular table.

• Arranging flowers in a circular vase.

Which of the following scenarios best illustrates a circular permutation?

• Arranging chairs in a row

• Arranging egg on a tray

• Arranging chairs around a circular table.

• Arranging clothes in a shelf.

1.       What is the key difference between linear and circular permutations?

• Linear permutations involve arranging objects in a straight line, while circular permutations involve arranging objects in a circle.

• Linear permutations involve arranging objects in a circle, while circular permutations involve arranging objects in a straight line.

• Linear permutations involve arranging objects in any order, while circular permutations involve arranging objects in a specific order.

• There is no difference between linear and circular permutations.

For items 4-5

In a group of 8 friends planning a road trip. They are deciding on the seating arrangements for their journey in both a circular and linear setting.

 

Questions:

 

1.      In how many different ways can the 8 friends be seated in a row of seats in the car for the road trip?

2.      If the car seats are arranged in a circular fashion, and two friends insist on sitting next to each other, how many distinct seating arrangements are possible?

• 40,320 and 5,040

• 40, 530 and 5,050

• 40, 540 and 5,050

• 40, 530 and 5,040

For items 4-5

In a group of 8 friends planning a road trip. They are deciding on the seating arrangements for their journey in both a circular and linear setting.

 

Questions:

 

1.      In how many different ways can the 8 friends be seated in a row of seats in the car for the road trip?

2.      If the car seats are arranged in a circular fashion, and two friends insist on sitting next to each other, how many distinct seating arrangements are possible?

• 40,320 and 5,040

• 40, 530 and 5,050

• 40, 540 and 5,050

• 40, 530 and 5,040