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Re: The number of ways in which 8 different flowers can be seated to form [#permalink]
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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)!

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