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 please help--counting w/ symmetry

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In how many distinct ways can I arrange my five keys on a keychain, if I want to put my house key next to my car key? Two arrangements are not considered different if the keys are in the same order (or can be made to be in the same order without taking the keys off the chain--that is, by reflection or rotation).

 Jun 20, 2018

3+0 Answers

 #1
avatar
+1

You have two places to start

House - car

car - House       then the next 3 spaces have 6 possibilities

 

2 x 6 = 12 ways.        My guess.

 Jun 21, 2018
 #2
avatar+194 
+1

My guess is 24

 Jun 21, 2018
 #3
avatar+118677 
+1

I think   3!*2 = 12 ways which takes care of rotation  BUT

to take of care of reflection maybe divide by 2 

 

So maybe 6 ways.

 

I am not sure though.....

 Apr 26, 2019

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