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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?

1. 1/8
2. 1
3. 7
4. 8

Correct answer: 7

Solution

There are C(8,3)=56 vertex triples; each forms a triangle with probability (1/2)^3=1/8. Expected triangles = 56*(1/8) = 7. Stored '1' is wrong; correct is 7.

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