How many functions $f : \{ 1,2 , \ldots , 10 \} \rightarrow \{ 1 , \ldots , 2000 \}$, which satisfy
$$f ( i + 1 ) - f ( i ) \geq 20 , \text { for all } 1 \leq i \leq 9 ,$$
are there?\\
(A) $10 ! \binom { 1829 } { 10 }$\\
(B) $11 ! \binom { 1830 } { 11 }$\\
(C) $\binom { 1829 } { 10 }$\\
(D) $\binom { 1830 } { 11 }$