# Counting Problem

1. Apr 12, 2005

### lesquestions

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.

2. Apr 12, 2005

### Hurkyl

Staff Emeritus
How many ways can you place the green one, then place the rest?

3. Apr 12, 2005

### lesquestions

um 3? lol I don't get it...

4. Apr 12, 2005

### HallsofIvy

Staff Emeritus
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?