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# The number of ways in which 8 different flowers can be seated to form

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Joined: 21 Jan 2007
Posts: 1856
Location: New York City
The number of ways in which 8 different flowers can be seated to form  [#permalink]

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Updated on: 08 Nov 2018, 04:24
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Difficulty:

75% (hard)

Question Stats:

34% (01:07) correct 66% (01:13) wrong based on 238 sessions

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The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated is:

A. 4!*4!

B. 288

C. 8!/4!

D. 5!*4!

E. 8!*4!

Originally posted by bmwhype2 on 03 Dec 2007, 08:43.
Last edited by Bunuel on 08 Nov 2018, 04:24, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Joined: 02 Sep 2009
Posts: 65764
The number of ways in which 8 different flowers can be seated to form  [#permalink]

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27 Jan 2010, 03:38
4
3
samrus98 wrote:
I feel 4! * 4! is not the final answer to this question. This number should be divided by 2 because a single garland when turned around gives us a different arrangement, but its still the same garland.

Answer: 4! * 4!/2 = 288
B

This is a good point.

There are two cases of circular-permutations:

1. If clockwise and anti clock-wise orders are different, then total number of circular-permutations is given by $$(n-1)!$$.

2. If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by $$\frac{(n-1)!}{2!}$$.

Specific garland (as I understand) when turned around has different arrangement, but its still the same garland as Samrus pointed out. So clock-wise and anti-clock-wise orders are taken as not different.

Hence we'll have the case 2: $$\frac{(5-1)!*4!}{2}=288$$
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Re: The number of ways in which 8 different flowers can be seated to form  [#permalink]

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05 Jan 2008, 08:00
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1
A

1. We have 5 different things: the group of 4 flowers and 4 separate flowers. 5P5=5!
2. to arrange the group of 4 flowers we have 4P4=4! ways. So, 5!*4!
3. circular symmetry means that variants with "circular shift" are the same variant. We can make 5 "circular shifts". Therefore, N=5!*4!/5=4!*4!
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Re: The number of ways in which 8 different flowers can be seated to form  [#permalink]

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25 Aug 2008, 12:51
1
1
bmwhype2 wrote:
The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated is:
A) 4!4!
B) 288
C) 8!/4!
D) 5!4!
E) 8!4!

[1234]5678

Assume that 1234 are alwasy together So. we can arrange themselves in 4! ways.
X5678
Now treat [1234]=X one single group we have 5 flower snad arrange in circular way= (5-1)!

4!*4!
A.
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Joined: 27 Oct 2008
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Re: The number of ways in which 8 different flowers can be seated to form  [#permalink]

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27 Sep 2009, 20:38
The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated is:
A) 4!4!
B) 288
C) 8!/4!
D) 5!4!
E) 8!4!

Soln. I too go with A.
(5-1)! * 4!
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Schools: NYU, NUS, ISB, DUKE, ROSS, DARDEN
Re: The number of ways in which 8 different flowers can be seated to form  [#permalink]

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28 Oct 2009, 09:56
3
1
I feel 4! * 4! is not the final answer to this question. This number should be divided by 2 because a single garland when turned around gives us a different arrangement, but its still the same garland.

Answer: 4! * 4!/2 = 288
B
Intern
Joined: 25 Jan 2010
Posts: 3
Re: The number of ways in which 8 different flowers can be seated to form  [#permalink]

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27 Jan 2010, 00:00
if 4 flowers must be toghter, we can think that at first we must seat that flowers in 5 seats, in that case ther are 5! cases, but we have 4flowers which in every case of 5! we can arrange its in 4! case, so there are 5!*4! cases
Re: The number of ways in which 8 different flowers can be seated to form   [#permalink] 27 Jan 2010, 00:00