1995 AHSME Problem 29

For how many three-element sets of distinct positive integers \{a,b,c\} is it true that a \times b \times c = 2310?

\mathrm{(A) \ 32 } \qquad \mathrm{(B) \ 36 } \qquad \mathrm{(C) \ 40 } \qquad \mathrm{(D) \ 43 } \qquad \mathrm{(E) \ 45 }

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.