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A complete graph with 6 vertices has $6\choose 2$$=15 edges, we have to choose at most 12 edges from these 15, i.e,$${15\choose0} + {15\choose1} + {15\choose2} + … + {15\choose12}=2^{15} – {15\choose13} – {15\choose14} – {15\choose15}= 32768 - 105 - 15 - 1= 32674$\$