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Circular Permutations Questions and Answers

Circular Permutations Questions

Formula

Definition of Circular Permutations

Permutation arrangements are of many types, they range from linear to circular. Circular arrangements are the type of permutations where the people or things are organized in a circle. In other terms, this arrangement is said to be circular in nature. For instance, imagine the roundtable meeting, creating a sort of necklet with various coloured beads. It looks like the things are arranged in a closed loop. Numerous ways of calculating related to the circular preparation gives rise to a circular arrangement or permutation. In the circular permutation, it is considered that one individual or thing is stable whereas the remaining people or things can be arranged.

Rules

Circular permutations can be a bit confusing as it completely different from the linear permutations or arrangement. The below mentioned rules will help to give you insights regarding the rules as well as the formulas in order to avoid any mistakes.
  • The numerous methods to organize different items along a stable (i.e., not able to chosen up out of the even and spun over) circle is: Pn =(n-1)!.
  • The number is (n-1)! as a substitute of the normal factorial n! as all cyclic arrangements of items are equal since the circle can be swapped.
  • The total number of permutations decreases to 1/2 (n – 1)! = 1/2 (4 – 1)! = 3!/2 = 3 when there is no reliance identified. The same will be the situation when the location of the individual or thing do not rely on the arrangement of the permutation. It is similar to the order of beads of the similar colour in a necklace.

Question 1

Time: 00:00:00
Find out the number of ways in which 5 members of a family can sit on a round table so that the grandparents always sit together.

24

24

50

50

100

100

200

200

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Question 2

Time: 00:00:00
Determine the ways in which 4 married couples are seated on a round table if the spouses sit opposite to one another.

48

48

36

36

45

45

60

60

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Question 3

Time: 00:00:00
Calculate the number of ways in which 10 beads of a necklace can be arranged?

181440

181440

118400

118400

181404

181404

18400

18400

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Question 4

Time: 00:00:00
Five people are sitting on a round table for meeting. These are P, Q, R, S, and T. In how many ways these people can be seated?

17

17

12

12

4

4

5

5

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Question 5

Time: 00:00:00
If Anita wants to arrange 3 Orange bangles, 5 Red bangles, and 2 Green bangles in a loop without any restrictions. Determine the number of ways it can be done.

236541

236541

362880

362880

230145

230145

None of the above

None of the above

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Question 6

Time: 00:00:00
A teacher needs to arrange the students of her classroom in two circles, one inside another. The inner-circle will have six members, and the outer circle will have 12 members. In how many ways these children can be arranged?

44545112

44545112

19958460

19958460

23569841

23569841

45789412

45789412

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Question 7

Time: 00:00:00
Determine the number of ways in which six people A, B, C, D, E, and F can be seated on a round table such that A and B always sit together.

240

240

120

120

300

300

320

320

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Question 8

Time: 00:00:00
Harry invited 20 people at a party. Determine the ways in which these people can be seated on a round table such that two specific people sit on either side of him.

20!

20!

16!

16!

18!

18!

19!*2

19!*2

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Question 9

Time: 00:00:00
Determine the ways in which 5 girls and 10 boys can be seated on a table so that girls always sit together.

11!*5!

11!*5!

10!*5!

10!*5!

10!

10!

5!

5!

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Question 10

Time: 00:00:00
Determine the ways in which 4 married couples are seated on a round table if the men and women must sit alternatively.

152

152

144

144

200

200

235

235

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Question 11

Time: 00:00:00
Find out the number of ways in which 3 people can be seated on a round table.

2

2

10

10

15

15

None of the above

None of the above

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Question 12

Time: 00:00:00
Calculate the number of garlands that can be made using 10 flowers when all of them are of different colors?

13125697

13125697

181440

181440

2362145

2362145

6987123

6987123

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Question 13

Time: 00:00:00
Determine the number of ways in which 20 people can be seated around a table if there are only 9 chairs.

362145112

362145112

1236514456

1236514456

2312456633

2312456633

6772147200

6772147200