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Find the number of garlands made by six distinct beads

Find the number of garlands made by six distinct beads 

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5 Answers

Ojas Jain
14 Points
12 years ago
Look either you can go by:-

Select any bead first- no of ways:6C1

Then arrange the others now because the symmetry is broken-no of ways:5!

But after writing this u will find that the same structure would be repeated because of the circular arrangement when u take another beads as starting point as thus forms a circular arrangement and thus it never end. It is a continuous arrangement 
Thus every structure is repeated 6 times, then divide throughout by 6 

The Ans is: 6x5!/5= 5! 

          OR
Another method for all such garland sums are (n-1)! Ehich is always valid for any of the circular arrangement
akash aggarwal
19 Points
12 years ago

5/2!

Anubhav Sharma
5 Points
12 years ago

accordingto you answer is coming 120 , but the actual answer given in my book is 60

Anubhav Sharma
5 Points
12 years ago

What is your approach ,your answer is right but how you calculated it

Ojas Jain
14 Points
12 years ago

That is becoz after getting 5! We see that the clockwise and anticlockwise arrangement is same

Thus the ans is 5!/2

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