Problem Solving

In a garden, seven flowers are to be arranged around a circular walk. Two arrangements of the flowers are considered different only when the positions of the flowers are different relative to each other. What is the total number of different possible arrangements of the flowers?

I obtained this question from
https://www.gmathacks.com/quant-topics/p ... ircle.html

but in my view the answer given is wrong.

The answer given is 720,
but shouldn't it be 360,

Solution:

n = 7

We can arrange this circular permutation in (n-1)! number of ways

Hence 6!
since the flowers are identical and will be the same from clockwise or counter-clockwise.

Answer is 6! / 2 = 360

Experts, please share your valued views.

eaakbari wrote:In a garden, seven flowers are to be arranged around a circular walk. Two arrangements of the flowers are considered different only when the positions of the flowers are different relative to each other. What is the total number of different possible arrangements of the flowers?

I obtained this question from
https://www.gmathacks.com/quant-topics/p ... ircle.html

but in my view the answer given is wrong.

The answer given is 720,
but shouldn't it be 360,

Solution:

n = 7

We can arrange this circular permutation in (n-1)! number of ways

Hence 6!
since the flowers are identical and will be the same from clockwise or counter-clockwise.

Answer is 6! / 2 = 360

Experts, please share your valued views.

For an explanation of circular permutations, check my post here:

https://www.beatthegmat.com/seating-arra ... 85488.html

We divide by 2 only if the elements are to be arranged around a RING THAT CAN BE FLIPPED OVER. I posted an explanation here:

https://www.beatthegmat.com/counting-methods-t73853.html

eaakbari wrote:In a garden, seven flowers are to be arranged around a circular walk. Two arrangements of the flowers are considered different only when the positions of the flowers are different relative to each other. What is the total number of different possible arrangements of the flowers?

I obtained this question from
https://www.gmathacks.com/quant-topics/p ... ircle.html

but in my view the answer given is wrong.

The answer given is 720,
but shouldn't it be 360,

Solution:

n = 7

We can arrange this circular permutation in (n-1)! number of ways

Hence 6!
since the flowers are identical and will be the same from clockwise or counter-clockwise.

Answer is 6! / 2 = 360

Experts, please share your valued views.

It is n!/n = 7!/7 = 720.