Eight men and six women sit around a table. How many sitting arrangeme

1.	Eight men and six women sit around a table. How many sitting arrangements will have no two women together?
Answer» 8 men can be seated around a table in (8 – 1)! = 7! ways. No two women should sit together. There are 8 gaps created by 8 men’s seats. ∴ Women can be seated in 8 gaps in P ways. ∴ Required number of arrangements = 7! x⁸P₆

Eight men and six women sit around a table. How many sitting arrangements will have no two women together?

Answer»

8 men can be seated around a table in (8 – 1)! = 7! ways.

No two women should sit together.

There are 8 gaps created by 8 men’s seats.

∴ Women can be seated in 8 gaps in P ways.

∴ Required number of arrangements = 7! x⁸P₆