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May 24, 2024Question 8761 – Algorithms
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?
Correct Answer: C
Question 50 Explanation:
Among available ‘8’ vertices, we need to identify the cycles of length ‘3’.
The probability that there exists one edge between two vertices = 1/2
So, the total probability that all three edges of the above exists
= 1/2 × 1/2 × 1/2 (as they are independent events)
= 1/8
Total number of ways in which we can select ‘3’ such vertices among ‘8’ vertices = 8C3 = 56
Total number of cycles of length ‘3’ out of 8 vertices = 56 × 1/8 = 7
The probability that there exists one edge between two vertices = 1/2
So, the total probability that all three edges of the above exists
= 1/2 × 1/2 × 1/2 (as they are independent events)
= 1/8
Total number of ways in which we can select ‘3’ such vertices among ‘8’ vertices = 8C3 = 56
Total number of cycles of length ‘3’ out of 8 vertices = 56 × 1/8 = 7
1/8
1
7
8
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