There are 4*3*2*1 = 24 ways.
However, if you consider ABCD as the same as DCBA - same neighbours, but left and right swapped - then there are only half as many.
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120 ways
How many different ways can we arrange 9 objects taken 3 at a time?
In 6 way
If the people are always facing forward? 24 ways.
in how many ways can a party of 8 people arrange themselves round a table?