# Number of arrangements possible?

+1 vote
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Neha has 6 flower pots, each having a unique flower. Pots are arranged in a row.
Neha rearrange the sequence each day but not two pots should be arranged
adjacent to each other which were already adjacent to each other in previous
arrangements. How many days she can do this or how many such arrangements is
possible ?

posted Dec 22, 2014
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## 2 Answers

+1 vote

Answer: 6
Number of different pairs possible: 6C2 = 30
In each arrangement 5 of them will be adjacent.
Therefore, total number of distinct arrangements = 30/5 = 6

General solution for n: nC2/(n-1)

answer Dec 24, 2014
0 votes

Is answer 35
- x - x - x
x can be changed within itself and - can be changed within itself so total 3! * 3! ie 36 and subtract the current one so total 35 ways.

But not very sure of answer :(

answer Dec 23, 2014
incorrect... try for n=4
only 2 arrangements are possible,
1234
1324
Yes you are right, for 4 say you start from
1234
then next possible combinations are 3214, 1432

So mine is wrong, post the answer in a day or two if you don't see the response further. But dimag kee batti jala dee nice problem...
i think you didn't get the question properly,,
if my initial arrangement is 1 2 3 4
then next arrangement cannot be 3 2 1 4 or 1 4 3 2
because in both these arrangements two elements are adjacent that were adjacent in earlier arrangement like (1 2 was adjacent in 1st arrangement which is also adjacent in 2nd arrangement which is not allowed ).
Looks like, please post the answer cant crack it :)

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