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I have a multiset $\left\{ {2,3,3,3,4,4,5,5,6,7} \right\}$. How many distinct multiplications of three numbers chosen from the multiset?

e.g. $2×3×3$; $2×3×4$; $4×4×3$;... not $2×3×3$; $3×3×2$;... and $4×3×3$; $6×2×3$; ... (equal multiplication) are considered as the same.

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    By "distinct multiplications", do you mean distinct factors, or distinct *results*? (E.g., are $2\times 3\times 3$ and $1\times 3\times 6$ "distinct multiplications", or the same one?)2011-05-15
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    You don't have a set; what you have is a multiset because there are repetitions.2011-05-15

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