1991 AHSME Problem 13

Horses X,Y and Z are entered in a three-horse race in which ties are not possible. The odds against X winning are 3:1 and the odds against Y winning are 2:3, what are the odds against Z winning? (By "odds against H winning are p:q" we mean the probability of H winning the race is \frac{q}{p+q}.)

\textbf{(A) } 3:20\qquad \textbf{(B) } 5:6\qquad \textbf{(C) } 8:5\qquad \textbf{(D) } 17:3\qquad \textbf{(E) } 20:3

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