How many ways can six friends be arranged around a circular dinner tab

How do we arrive at 6!/6? I had chosen the answer for 6! only. What is the logic behind this please?

ways in which 6 friends can sit around a circular table = (6-1)! = 5! = 120
Correct Answer - D
I wouldn't explain the logic again chetan has done it already very well

Formula to arrange \(n\) distinct objects in circle \(= (n−1)!\)

Number of ways 6 friends can be arranged around a circular dinner table \(= (6 -1)! = 5!\)

\(5! = 5*4*3*2*1 = 120\)

Answer (D)...

Since we are seating 6 people around a circle, the people can be arranged in (6-1)! = 5! = 120 ways.

Answer: D

For a circle the formula departs from the traditional method so instead of 6! the formula is 5! (n-1!)

D

OA:D

Number of ways six friends can be arranged around a circular dinner table \(=\frac{n!}{n}=\frac{6!}{6}=5!=120\)

for any circular combination formulation is always : (n-1)!
so here n = 6
5! = 120
there are 120 ways in which 6 friends can be arranged around a circular table

Thank you for explaining the logic behind 6!/6.

I am not the type of person who can just "memorize" a formula without understanding the logic behind it.

Hope the GMATClub community can benefit from my takeaway.

I got the wrong answer today, because I used the 6! formula which turns out to be the wrong logic as per your explanation.
Should similar question appears on the exam, I must get this type of question right.
Action item for exam: in a time-pressured situation, BE VERY CLEAR what the question is asking you for. Does it make sense for 6! ? Are you sure you are not double-counting any arrangement ? Draw it out (especially when you are not sure about which formula to use).

number of ways n people can be arranged in a circular table = \((n-1)!\)

\(6 friends = (6-1)! = 5! = 120\)

Answer is D.

for n object circular arrangement can be done in (n-1)! ways
so for 6 people circular arrangement can be done in (6-1)! =5! =5×4×3×2=120 ways

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