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Find the number of garlands made by six distinct beads

Find the number of garlands made by six distinct beads 

Grade:

5 Answers

Ojas Jain
14 Points
9 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
9 years ago

5/2!

Anubhav Sharma
5 Points
9 years ago

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

Anubhav Sharma
5 Points
9 years ago

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

Ojas Jain
14 Points
9 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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