Circular Permutations and Combinations

In how many ways can 5 people be seated around a circular table?

• 30
• 20
• 12
• 24

How many ways can 7 distinct objects be arranged in a circle?

• 720
• 1000
• 120
• 504

If 6 friends sit around a circular table, how many distinct arrangements exist?

• 720
• 60
• 30
• 120

A necklace has 8 beads of different colors. In how many ways can they be arranged?

• 5040
• 720
• 1280
• 2520

How many ways can 4 people be arranged in a circle if two must always sit together?

• 6
• 12

• 8
• 4

If two people must always sit together in a circular arrangement, we treat them as a single unit.

• true

• false

In circular permutations, the first position is always fixed.

• true

• false

Five people are to be seated in a circular manner. How many distinct arrangements are possible?

(a)  

A group of 8 friends is sitting around a round table. One of them insists on sitting in a specific seat. How many ways can the rest be seated?

(a)  

A bracelet is made using 5 different beads. How many distinct arrangements can be made if flipping the bracelet is considered the same arrangement?

(a)