Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to
A
15
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B
30
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C
90
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D
360
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Solution
The correct option is D 360 The graph given is K6.
In K6, every cycle of length 4 corresponds to selecting 4 vertices out of 6 vertices, which can be done in 6C4 ways and then ordering the 4 vertices in circular permutation in 3! ways (since vertices are labeled). So final answer is 6C4×3!=90.