Let $A = \left\{ x _ { 1 } , x _ { 2 } , \ldots , x _ { 50 } \right\}$ and $B = \left\{ y _ { 1 } , y _ { 2 } , \ldots , y _ { 20 } \right\}$ be two sets of real numbers. What is the total number of functions $f : A \rightarrow B$ such that $f$ is onto and $f \left( x _ { 1 } \right) \leq f \left( x _ { 2 } \right) \leq \cdots \leq f \left( x _ { 50 } \right)$ ?\\
(A) $\binom { 49 } { 19 }$\\
(B) $\binom { 49 } { 20 }$\\
(C) $\binom { 50 } { 19 }$\\
(D) $\binom { 50 } { 20 }$