Circular Permutation
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Q.
Three boys and three girls are to be seated around a round table in a circle.
Among them the boy does not want any girl neighbor and the girl does not want any boy neighbor then the number of such arrangements is ?
Q.
Six teachers and six students have to sit around a circular table such that there is a teacher between any two students. The number of ways in which they can sit is
None of these
Q. Let R={(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A={3, 6, 9, 12}. Then the relation is
- Reflexive and transitive only
- Reflexive only
- Reflexive, symmetric and transitive
- Reflexive but neither symmetric nor transitive
Q.
The number of ways in which persons can go in two boats so that there may be on each boat, supposing that two particular persons will not go in the same boat?
None of these
Q. Twelve persons are to be arranged around two round tables such that one table can accommodate seven persons and another table can accommodate five persons only.
The total number of ways in which these 12 persons can be arranged is
The total number of ways in which these 12 persons can be arranged is
- 12C7×6!×4!
- 6!×4!
- 13C5×6!×4!
- 2 12C7×6!×4!
Q. The number of ways in which six men and five women can dine at a round table if no two women are to sit together is given by
- 6!×5!
- 30
- 5!×4!
- 7!×5!
Q. There are 2 brothers among a group of 20 persons. The number of ways the group can be arranged around a circle so that there is exactly one person between the two brothers is
- 2×17!
- 18!×18
- 2×18!
- 2×17!×17
Q. A group of 10 persons including ''Manager'', ''Assistant manager'' and ''Secretary'' are to be seated around a circular table.
The total number of possible arrangements, if ''Manager'' and ''Secretary'' had to sit together and ''Assistant manager'' had to sit opposite to ''Manager'' is
The total number of possible arrangements, if ''Manager'' and ''Secretary'' had to sit together and ''Assistant manager'' had to sit opposite to ''Manager'' is
- 2×8!
- 8!
- 2×7!
- 3×8!
Q. Number of ways in which 10 different diamonds can be arranged to make a necklace is
- 9!
- 10!2
- 9!2
- 10!
Q. How many garlands can be formed using 10 different flowers?
- 9!2
- 10!2
- 10!
- 10!×2!
Q. If 8 persons A, B, C, D, E, F, G, H are to be seated around a circular table, then the number of possible arrangements
- without any restriction is 7!
- when A and B should be seated together is 6!
- when A and B should be seated opposite to each other is 6!
- when there should be exactly two persons between A and B is 720
Q. The total number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour, is
- 6×(9!)2
- 11!
- 4×(8!)2
- 5×(9!)2
Q. Twelve persons are to be arranged around two round tables such that one table can accommodate seven persons and another table can accommodate five persons only.
The total number of possible arrangements if two particular persons A and B do not want to be on the same table is
The total number of possible arrangements if two particular persons A and B do not want to be on the same table is
- 10C4×6!×4!
- 2× 10C6×6!×4!
- 11C6×6!×4!
- 2× 11C4×6!×4!
Q. 5 boys and 5 girls had to sit alternately around a round table. This can be done in N ways. Then the value of N is
Q. Twelve persons are to be arranged around two round tables such that one table can accommodate seven persons and another five persons only.
The number of ways of arrangement if two particular persons A and B want to be together and consecutive is
The number of ways of arrangement if two particular persons A and B want to be together and consecutive is
- 10C76!3!2!+ 10C54!5!2!
- 10C56!3!+ 10C74!5!
- 10C76!2!+ 10C55!2!
- none of these
Q. In a playground, 3 sisters and 5 other girls are playing together. The number of ways in which all the girls be seated in a circular order so that the three sisters are not seated together is
- 5040
- 4920
- 4320
- 2160
Q. A team of 8 person including ''Captain'' and ''Vice-captain'' are to be seated around a circular table, then the number of possible arrangements
- without any restriction is 7!
- when ''Captain'' and ''Vice-captain'' should be seated opposite to each other is 5!
- when there should be atleast one person between ''Captain'' and ''Vice-captain'' is 5×6!
- when there should be exactly one person between ''Captain'' and ''Vice-captain'' is 12×5!
Q. A group of 10 persons including ''Manager'', ''Assistant manager'' and ''Secretory'' are to be seated around a circular table.
The total number of possible arrangements, if ''Manager'', ''Assistant manager'' and ''Secretory'' had to sit together is
The total number of possible arrangements, if ''Manager'', ''Assistant manager'' and ''Secretory'' had to sit together is
- 9!
- 8!
- 3!×8!
- 3!×7!
Q. There are 6 boys and 5 girls. There are two round tables with 7 chairs and 4 chairs.
- Number of ways of arranging all of them is 11!28
- Number of ways of arranging all of them so that all girls are at same table is (6!)28
- Number of ways of arranging all of them so that all boys are at same table is 5! 6!4
- Number of ways of arranging all of them so that all boys are at one table or all girls are at one table is 6!(120)
Q. The number of ways in which 8 red roses and 5 white roses of different sizes can be made out to form a garland so that no two white roses come together is
- 8!2.8P5
- 7!2.8P5
- 7!2.9P5
- 7!4P3
Q. A team of 8 person including ''Captain'' and ''Vice-captain'' are to be seated around a circular table, then the number of possible arrangements
- without any restriction is 7!
- when ''Captain'' and ''Vice-captain'' should be seated opposite to each other is 5!
- when there should be atleast one person between ''Captain'' and ''Vice-captain'' is 5×6!
- when there should be exactly one person between ''Captain'' and ''Vice-captain'' is 12×5!
Q. The number of ways in which 3 boys and 12 girls can be seated around a circle such that there are atleast 3 girls between any two is 20×k!, then k is
Q. Three boys and three girls are to be seated around a circular table. Among them, the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. Then the number of possible arrangements is
- 4
- 6
- 8
- 10
Q. Six persons A, B, C, D, E, F are to be seated at a circular table. If A should have either B or C on his immediate right and B must always have either C or D on his immediate right, then the total number of possible arrangements is
Q. A team of 8 person including ''Captain'' and ''Vice-captain'' are to be seated around a circular table, then the number of possible arrangements
- without any restriction is 7!
- when ''Captain'' and ''Vice-captain'' should be seated opposite to each other is 5!
- when there should be atleast one person between ''Captain'' and ''Vice-captain'' is 5×6!
- when there should be exactly one person between ''Captain'' and ''Vice-captain'' is 12×5!