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Jon has five flowers, each a different color. He wants to arrange them

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Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post Updated on: 08 Jun 2018, 02:55
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Question Stats:

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Jon has five flowers, each a different color. He wants to arrange them around the circumference of a circular vase. How many distinct arrangements can he make?

A) 20
B) 24
C) 25
D) 60
E) 120

Any advice/help would be greatly appreciated!

Originally posted by neiln413b on 07 Jun 2018, 13:26.
Last edited by Bunuel on 08 Jun 2018, 02:55, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post 07 Jun 2018, 13:38
neiln413b wrote:
Hi, need help with this problem solving permutation/combination problem below:

Jon has givefive? flowers, each a different color. He wants to arrange them around the circumference of a circular vase. How many distinct arrangements can he make?

A) 20
B) 24
C) 25
D) 60
E) 120

Any advice/help would be greatly appreciated!

Hi neiln413b,

Arrangements in line n!,and arrangements around the circumference (n-1)!
In our case it is (5-1)!=4!=4*3*2*1=24. Answer B.
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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post 07 Jun 2018, 14:43
Thanks for the quick response! Yes I meant to say 5.

So the formula for circumference (n-1)! always applies?
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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post 07 Jun 2018, 23:28
neiln413b wrote:
Hi, need help with this problem-solving permutation/combination problem below:

Jon has five flowers, each a different color. He wants to arrange them around the circumference
of a circular vase. How many distinct arrangements can he make?

A) 20
B) 24
C) 25
D) 60
E) 120

Any advice/help would be greatly appreciated!


The direct formula for arrangements in a circular order is (n-1)!, hence the answer is 4! = 24

To understood the concept use the link below:
https://gmatclub.com/forum/combinatorics-made-easy-206266.html#p1579452

Thanks,
GyM
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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post 08 Jun 2018, 02:56
neiln413b wrote:
Thanks for the quick response! Yes I meant to say 5.

So the formula for circumference (n-1)! always applies?


21. Combinatorics/Counting Methods



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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post 12 Jun 2018, 11:08
neiln413b wrote:
Jon has five flowers, each a different color. He wants to arrange them around the circumference of a circular vase. How many distinct arrangements can he make?

A) 20
B) 24
C) 25
D) 60
E) 120


We use the circular permutations formula: (n - 1)!. Thus, the total number of ways to arrange the flowers is (5 - 1)! = 4! = 24.

Answer: B
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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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New post 05 Jul 2018, 09:59
The logic for circular arrangements is that you don't have a reference point until you arrange the first object. Once you have fixed the position of the first object then the remaining (n-1) objects can be arranged in (n-1)! ways.

In our case it is (5-1)!=4!=24 ways.

Correct Answer is option B.
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Re: Jon has five flowers, each a different color. He wants to arrange them &nbs [#permalink] 05 Jul 2018, 09:59
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