
Arnold F. answered 02/12/16
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College Professor & Expert Tutor In Statistics and Calculus
In a circle the answer should be 5040.
When you line the dogs up you have a first and last dog so there are 8! ways.
In a circle there is no "first" dog. So you arbitrarily pick a "first" dog. Once that dog is selected (you do not need to use the number 8 here) there are 7 dogs left and the answer should be 7!.
Consider if there were 3 dogs there would be six (3!) ways to line them up, but in a circle ABC is the same as BCA is the same as CAB so the only other circular way is ACB; 2!.
Any questions? comment back.