In how many ways can 4 couples be seated around a circular table so that men and women sit alternately? (Assume each couple is man+woman; total 8 people.)
In how many ways can 4 couples be seated around a circular table so that men and women sit alternately? (Assume each couple is man+woman; total 8 people.)
In how many ways can 5 men and 5 women be seated alternately around a circle?
In how many ways can 5 men and 5 women be seated alternately around a circle?
In how many ways can 6 people be seated around a circle such that two particular people sit with exactly one person between them (i.e., one seat separating them both clockwise or anticlockwise)?
In how many ways can 6 people be seated around a circle such that two particular people sit with exactly one person between them (i.e., one seat separating them both clockwise or anticlockwise)?
From 10 people seated around a round table, in how many distinct ways can we choose two people who sit next to each other?
From 10 people seated around a round table, in how many distinct ways can we choose two people who sit next to each other?
In a circular arrangement of 9 people, how many arrangements are there such that two particular people sit together?
In a circular arrangement of 9 people, how many arrangements are there such that two particular people sit together?
(Valid) Eight people A, B, C, D, E, F, G, H sit around a circle facing centre. A is second to the left of B. C is immediate left of B. D is opposite B. Who is immediate right of D?
(Valid) Eight people A, B, C, D, E, F, G, H sit around a circle facing centre. A is second to the left of B. C is immediate left of B. D is opposite B. Who is immediate right of D?
10 people are to be seated around a table. How many circular arrangements are possible if rotations are considered identical but reflections are considered different?
10 people are to be seated around a table. How many circular arrangements are possible if rotations are considered identical but reflections are considered different?
Eight people are seated around a circle. In how many ways can they be seated if two particular people must sit opposite each other?
Eight people are seated around a circle. In how many ways can they be seated if two particular people must sit opposite each other?
In how many ways can 6 people sit in a circle if two particular people must sit opposite each other?
In how many ways can 6 people sit in a circle if two particular people must sit opposite each other?
In a circular seating of 8 people facing the centre, how many ways can we seat them so that men and women alternate, given 4 men and 4 women?
In a circular seating of 8 people facing the centre, how many ways can we seat them so that men and women alternate, given 4 men and 4 women?
In how many ways can 4 couples (8 people) be seated around a circular table so that no couple sits together?
In how many ways can 4 couples (8 people) be seated around a circular table so that no couple sits together?
Number of circular arrangements of n distinct persons where seating arrangements that can be rotated into each other are considered identical is:
Number of circular arrangements of n distinct persons where seating arrangements that can be rotated into each other are considered identical is:
In a circular seating of 6 people facing centre, A sits third to the left of B. If B is fixed at a reference seat, where is A?
In a circular seating of 6 people facing centre, A sits third to the left of B. If B is fixed at a reference seat, where is A?
Six persons A–F are to be seated around a circular table. If rotations are identical but reflections are different, how many arrangements are there where A and B are opposite?
Six persons A–F are to be seated around a circular table. If rotations are identical but reflections are different, how many arrangements are there where A and B are opposite?
Eight friends A, B, C, D, E, F, G, H sit around a circular table facing centre. B sits third to the left of A. D sits immediate right of A. C sits between D and E. G sits opposite B. Who sits immediate left of G?
Eight friends A, B, C, D, E, F, G, H sit around a circular table facing centre. B sits third to the left of A. D sits immediate right of A. C sits between D and E. G sits opposite B. Who sits immediate left of G?
In how many ways can we seat 4 boys and 4 girls around a table such that no two girls sit together?
In how many ways can we seat 4 boys and 4 girls around a table such that no two girls sit together?
In how many ways can 9 people be seated around a circle so that 3 particular people always sit together (in any order)?
In how many ways can 9 people be seated around a circle so that 3 particular people always sit together (in any order)?
Seven friends A, B, C, D, E, F, G sit around a circular table facing the centre. A is second to the left of B. C is immediate left of B. D is opposite B. Who is immediate right of D?
Seven friends A, B, C, D, E, F, G sit around a circular table facing the centre. A is second to the left of B. C is immediate left of B. D is opposite B. Who is immediate right of D?
Six people A-F are seated around a circle facing centre. A sits opposite D. B sits immediate left of A. C sits immediate right of D. Who sits between B and C (in clockwise direction)?
Six people A-F are seated around a circle facing centre. A sits opposite D. B sits immediate left of A. C sits immediate right of D. Who sits between B and C (in clockwise direction)?
Six persons A, B, C, D, E, F sit around a circle facing the centre. A sits opposite B. C sits immediate left of B. D sits immediate right of A. E is not adjacent to A. Who sits to the immediate right of C?
Six persons A, B, C, D, E, F sit around a circle facing the centre. A sits opposite B. C sits immediate left of B. D sits immediate right of A. E is not adjacent to A. Who sits to the immediate right of C?
If reflections (mirror images) are also considered identical (i.e., clockwise and anticlockwise orders are the same), number of distinct arrangements of n distinct people around a round table is:
If reflections (mirror images) are also considered identical (i.e., clockwise and anticlockwise orders are the same), number of distinct arrangements of n distinct people around a round table is:
In how many ways can 4 men and 3 women be seated around a circular table so that no two women sit together?
In how many ways can 4 men and 3 women be seated around a circular table so that no two women sit together?
In a circular arrangement of 10 people, how many seating arrangements have two specified people sitting with exactly one person between them (on one side or the other — i.e., there is exactly one seat separating them, either clockwise or anticlockwise)?
In a circular arrangement of 10 people, how many seating arrangements have two specified people sitting with exactly one person between them (on one side or the other — i.e., there is exactly one seat separating them, either clockwise or anticlockwise)?
Six friends are seated around a table. How many seating arrangements are possible if two specific persons must not be opposite each other (table has even seats so 'opposite' is defined)?
Six friends are seated around a table. How many seating arrangements are possible if two specific persons must not be opposite each other (table has even seats so 'opposite' is defined)?
If 7 persons are to be seated around a circular table, in how many ways can this be done so that two particular persons are always opposite to each other?
If 7 persons are to be seated around a circular table, in how many ways can this be done so that two particular persons are always opposite to each other?