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)?
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)?
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)?
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?
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?
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?
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?
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?
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 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?
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)?
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?
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?
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?
(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?
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)?
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 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?
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?
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?
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?
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 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 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?