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How many ways can you arrange 8 pieces of fruit?

 Jul 8, 2014

Best Answer 

 #2
avatar+576 
+8

8!=8*7*6*5*4*3*2*1=40,320.

Think of there being 8 different places that you can put a single piece of fruit.  when you first start pick a spot, there are 8 different options you have for putting a piece there.  Once you place it you move to the second spot, you now have seven pieces of fruit left to pick from because one was already used.  Go to the third spot, now you only have 6 pieces to pick from.  This continues until you run out of fruit and places to put it.

 Jul 8, 2014
 #1
avatar+124676 
+8

Assuming that they are all different types.....8!  = 40320 ways....!!!!

 

  

 Jul 8, 2014
 #2
avatar+576 
+8
Best Answer

8!=8*7*6*5*4*3*2*1=40,320.

Think of there being 8 different places that you can put a single piece of fruit.  when you first start pick a spot, there are 8 different options you have for putting a piece there.  Once you place it you move to the second spot, you now have seven pieces of fruit left to pick from because one was already used.  Go to the third spot, now you only have 6 pieces to pick from.  This continues until you run out of fruit and places to put it.

jboy314 Jul 8, 2014
 #3
avatar+124676 
+5

Let me add one thing to this answer......this is assuming a "linear" arrangement. It the fruit were arranged in a circle, the answer would be just 7! = 5040.

To see this, note that I could "anchor" one piece of fruit in any position on the circle. Then, I have seven ways to choose the next piece of fruit, 6 ways to choose the next, etc.

 

  

 Jul 8, 2014
 #4
avatar+118139 
+5

That is assuming that the fruit is all differerent and arranged in a straight line.  8!

If it was arranged around a circular platter then it would be 7!

If they were just randomly placed in the universe then the number of possibilities would be infinite!

I'm sorry - I just realised that Chris said some of this already.

 Jul 10, 2014

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