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Omni-MATH / Jody has 6 distinguishable balls and 6 distinguishable sticks, all of the same…

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problem

Jody has 6 distinguishable balls and 6 distinguishable sticks, all of the same length. How many ways are there to use the sticks to connect the balls so that two disjoint non-interlocking triangles are formed? Consider rotations and reflections of the same arrangement to be indistinguishable.

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