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

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Intern
Joined: 13 Aug 2017
Posts: 8
Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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Updated on: 08 Jun 2018, 01:55
2
00:00

Difficulty:

25% (medium)

Question Stats:

64% (00:35) correct 36% (00:48) wrong based on 116 sessions

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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, 12:26.
Last edited by Bunuel on 08 Jun 2018, 01:55, 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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07 Jun 2018, 12:38
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.
Intern
Joined: 13 Aug 2017
Posts: 8
Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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07 Jun 2018, 13:43
Thanks for the quick response! Yes I meant to say 5.

So the formula for circumference (n-1)! always applies?
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Joined: 14 Dec 2017
Posts: 518
Location: India
Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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07 Jun 2018, 22:28
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:

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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08 Jun 2018, 01:56
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Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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12 Jun 2018, 10:08
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.

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Posts: 618
Re: Jon has five flowers, each a different color. He wants to arrange them  [#permalink]

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05 Jul 2018, 08:59
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.

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Re: Jon has five flowers, each a different color. He wants to arrange them &nbs [#permalink] 05 Jul 2018, 08:59
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