$FNP$ ,$ \#P$,$\oplus P$ classes
1)$\bf FNP$ is contained in $\bf FPH$, which is called the "functional polynomial hierarchy", where every function in $\bf FPH$  is polynomial time 1-Turing reduciable to some function in $\bf \#P$. 
2)We know from the Valiant Vazirani theorem that $\bf NP$ $\subseteq$ $\bf RP^{PromiseUP}$. We also know that $\bf UP$ $\subseteq$ $\bf \oplus P$. Therefore, we have $\bf NP$ $\subseteq$ $\bf RP^{\bf \oplus P}$.