Question

our friends met every week to play cards, using a table with five chairs. Eventually, they realized they had chosen a different seating arrangement each week and had exhausted every possibility. How long had the friends played cards together?

Answer 1

If the table is circular, they played cards for 24 weeks.

If the table is rectangular, they played cards for 120 weeks.

Explanation:

Five friends met every week to play cards, using a table with five chairs. Eventually, they realized they had chosen a different seating arrangement each week and had exhausted every possibility.

It means they have used all possible way to arrange five people in a circle.

For circular table, then total ways to arrange 5 people on a circular table = (5-1)! = 4! = 4x3x2x1 = 24 ways.

For rectangular table, then total ways = 5! = 5x4x3x2x1 = 120 ways.