In how many different ways can 20 different pearls be arranged to form a

Question:

In how many different ways can 20 different pearls be arranged to form a necklace?

 

Solution:

We know that necklace in the form of a circle, So we need to arrange 20 pearls in Circle

20 pearls can be arranged by $19 !$

Now each pearl have the same neighbour in the clockwise and anticlockwise arrangement

Total number of arrangement are $(19 !) / 2$

 

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