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

Question

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!

Bunuel · Accepted Answer

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

walker · Answer

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!

x2suresh · Answer

5678

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

4!*4!
A.

srivas · Answer

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!

samrus98 · Answer

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

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

Araik · Answer

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

Blanc123 · Answer

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?

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

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

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