Algebra
Find the number of garlands made by six distinct beads
Find the number of garlands made by six distinct beads
5 Answers
Ojas Jain
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!
ORAnother method for all such garland sums are (n-1)! Ehich is always valid for any of the circular arrangement
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!
ORAnother method for all such garland sums are (n-1)! Ehich is always valid for any of the circular arrangement
akash aggarwal
5/2!
Anubhav Sharma
accordingto you answer is coming 120 , but the actual answer given in my book is 60
Anubhav Sharma
What is your approach ,your answer is right but how you calculated it
Ojas Jain
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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algebra
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