PUMaC 2010 Combinatrics B Problem 3

Let \underline{x y z} represent the three-digit number with hundreds digit x, tens digit y, and units digit z, and similarly let \underline{y z} represent the two-digit number with tens digit y and units digit z. How many three-digit numbers \underline{a b c}, none of whose digits are 0, are there such that \underline{a b}>\underline{b c}>\underline{c a}?