NIELIT 2017 DEC Scientist B - Section B: 23

Question

Let $G$ be a complete undirected graph on $8$ vertices. If vertices of $G$ are labelled, then the number of distinct cycles of length $5$ in $G$ is equal to:

• A. $15$
• B. $30$
• C. $56$
• D. $60$

Comments

https://gateoverflow.in/473/gate-cse-2012-question-38

Answer 1

672 will be the answer

 FROM 8 vertices we can select 5 vertices in 8C5 ways=56 ways

HERE we have to make the CYCLE of length 5 so DISTINCT CYCLE possible =(n-1)!/2 =(5-1)!/2=12

so no of distinct  cycle of length 5=672

Comments

Yes ! this is correct ! but  not in options so one can infer that question setter is not interested in arrangements of these vertices once you choose them $\therefore \frac{672}{12} = 56$

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@ saxena0612

yes i agree but the problem is that they blindly copy the previous gate question without rectify then not here specificly many places also

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How to calculate number of distinct cycles ?

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@y RajuSri 

see above sol i have mentioned take cyclic permutation

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@saxena0612 what do you mean by “arrangements of these vertices once you choose them”?