If $\left| G \right| = p^aq^b$, then $G$ has a normal Sylow $p$-subgroup.

Question

Let $p,q$ primes with $\gcd (p,q) = 1$ and $a,b$ integers with $b < p-1$. I've tried to use the Sylow's third theorem but I can't show why $n_{p}$ can only be $1$, where $n_{p}$ is the number of Sylow $p$-subgroups of $G$.