*Discrete Math Help Needed* Suppose we have 5 flower pots, arranged in a circle, and 10 plants. How many different arrangements of 5 plants are there, where a single plant goes in every pot and two arrangements are considered the same if every plant has the same neighbors to its left and right?

Question

anonymous · Answer

Don't understand why the question is worded so that you have a few pots, but many plants?!

anonymous · Answer

Yeah me neither really.. I guess so you'll have more options?

anonymous · Answer

I was thinking it would be like this for the first part:
10! / (5!5!)

anonymous · Answer

= 252

anonymous · Answer

But I'm not sure on the second part..

anonymous · Answer

" where a single plant goes in every pot and two arrangements are considered the same if every plant has the same neighbors to its left and right?"

anonymous · Answer

Not sure; usually you have 5 ways for the first plant, 4, the next, and on and on; I don't know if that method applies to this type. My text book doesn't have this specific type of question.

anonymous · Answer

Yeah mine either..

anonymous · Answer

everyone in my class is stuck on this one.

anonymous · Answer

I think one of your classmates posted on the internet:
I can't think why they're mentioning 10 plants,
when the question has to do with only 5 plants.
Are they asking us to CHOOSE 5 plants from the set of 10?
The question is slightly ambiguous, and therefore completely illegitimate.

However, I'm going to assume that they mean 5 plants are to be chosen
from among the 10 available. In that case, the selection of the 5 gives us
(10!) / [ 5! 5! ] possibilities even before we start arranging the plants.
That is, there are 10x9x8x7x6 / 5x4x3x2x1 ways of just CHOOSING what
set of plants will be arranged. This number comes out to 9x7x4 = 252.

Next, when the 5 plants have been chosen, the selection of a pot for the
first one is arbitrary. Then there are 4 possibilities for its left-hand neighbor,
3 possibilities for its right-hand neighbor, and 2 possibilities for the LH neighbor
of its LH neighbor. Thus, once the 5 plants have been chosen, there are
only 12 distinct ways of arranging them.

So my final answer is 252 x 12 = 3024

anonymous · Answer

That is an answer I found at Yahoo answers.