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Ben has a collection of 14 stuffed animals (Alvin the Chipmunk, Belle the Bobcat, Craig the Crab, etc. down to Newt the Newt. He keeps them in alphabetical order in a long line on his shelf. One day after taking them down to play with for a while Ben decides to put them back and  he wonders how many ways he could put them back if each animal needed to be back in its original position or directly to the left or right of its original position. So, for example, Belle could either stay in the second place or be in Alvin or Craig's place in the new arrangement. How many different ways can Ben put the animals back on the shelf under this scheme?

 Jul 10, 2018

I'll just look for a pattern


2 animals 2 ways

3 animals 3! ways

4 animals 


b ac c can go anywhere   3*3*2*2 = 36 ways



If A goes to the middle then   BC (or CB) A DE(or ED)    4  

If A stays put 36 ways

If A goes second  


Now it is already getting all too much.

 Jul 17, 2018

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