If a random variable X follows the Binomial distribution B (33,p) such that $3P(X=0)=P(X=1),$ then the value of $\frac{P(X=15)}{P(X=18)}-\frac{P(X=16)}{P(X=17)}$ is equal to 

n = 33, let probability of success is p and q = 1-p
 $3p(x=0)=p(x=1)$
 ${3.}^{33}{C}_0{\left(q\right)}^{33}{=}^{33}{C}_{1}p{q}^{32}$
 $p=\frac{1}{12},q=\frac{11}{12},\frac{q}{p}=11$
$\frac{p(x=15)}{p(x=18)}-\frac{p(x=16)}{p(x=17)}$ 
 $\frac{{ }^{33}{C}_{15}{p}^{15}{q}^{18}}{{ }^{33}{C}_{18}{p}^{18}{q}^{15}}-\frac{{ }^{33}{C}_{16}{p}^{16}{q}^{17}}{{ }^{33}{C}_{17}{p}^{17}{q}^{16}}={\left(\frac{q}{p}\right)}^3-\left(\frac{q}{p}\right)$
 $={\left(11\right)}^3-11$
 $=1320$