Solving 5-Stone Counting Problem w/ Restrictions

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Homework Help Overview

The problem involves arranging 5 differently colored stones with a specific restriction on the placement of the green stone. The original poster is unsure how to incorporate the restriction that the green stone cannot be placed at the front or back of the sequence.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore how to account for the restriction on the green stone's placement and discuss potential arrangements based on its allowed positions. There are questions about the total number of arrangements and how to calculate them given the constraint.

Discussion Status

The discussion is ongoing, with some participants suggesting specific placements for the green stone and asking how many arrangements can be made for the other stones in those scenarios. There is no clear consensus yet, but various approaches are being considered.

Contextual Notes

The original poster references a solution from the back of the book, indicating a possible answer of 72 arrangements, which may influence the discussion on how to arrive at that number.

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Hi, I wasn't sure how to approach this problem:

You have 5 differently colored stones-red, orange, blue, green, purple. If the green stone cannot be placed at the front or the back of the sequence, how many possible arrangements can you make?

I know that without the above restriction, the amount would be 5!=120.

But I don't get how to use the restriction.

BTW the back of the book says that the answer is 72.

Help please! thanks.
 
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How many ways can you place the green one, then place the rest?

P.S. please don't multiple post.
 
um 3? lol I don't get it...
 
The DO it.

Suppose you place the green stone in the second place. How many different ways are there to place the other 4 stones?

Suppose you place the green stone in the third place. How many different ways are there to place the other 4 stones?

Suppose you place the green stone in the fourth place. How many different ways are there to place the other 4 stones?

Okay, now how many ways is that all together?
 

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