AHSME 1991 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 $\frac{q}{p+q}$.) $\text{(A) } 3:20 \text{(B) } 5:6 \text{(C) } 8:5 \text{(D) } 17:3 \text{(E) } 20:3$