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GATE | GATE CS 2013 | Question 24

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Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
 

(A)

7
 

(B)

1
 

(C)

1/8
 

(D)

8
 



Answer: (A)

Explanation:

A cycle of length 3 can be formed with 3 vertices. There can be total 8C3 ways to pick 3 vertices from 8. The probability that there is an edge between two vertices is 1/2. So expected number of unordered cycles of length 3 = (8C3)*(1/2)^3 = 7


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Last Updated : 28 Jun, 2021
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