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Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
27 Jan 2010, 04:38
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Expert Reply
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: \(\frac{(5-1)!*4!}{2}=288\)
Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
05 Jan 2008, 09:00
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Expert Reply
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!
Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
25 Aug 2008, 13:51
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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)!
Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
27 Sep 2009, 21:38
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!
Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
28 Oct 2009, 10:56
3
Kudos
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.
Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
27 Jan 2010, 01:00
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 Answer is D
Re: The number of ways in which 8 different flowers can be seated to form
[#permalink]
06 Aug 2020, 09:38
Bunuel wrote:
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: \(\frac{(5-1)!*4!}{2}=288\)
Hi, I am new here and do not have much experience with forum discussions and solving GMAT problems as well. But here's my point of view. (I'll appreciate if you tell me why I might be wrong.) I don't think clock-wise and anti-clock-wise arrangements are applicable for garlands. It's decorated with those flowers only on its front side. You don't normally turn it around and hang it backward. So anti-clockwise arrangement should not be even considered. It's similar to arrangements of people sitting around the table. You don't normally think of clock or anti-clockwise arrangements here, cause you can't turn the table around. So I think the OA to the problem is correct. Am I wrong here?
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Re: The number of ways in which 8 different flowers can be seated to form [#permalink]