If $^{20}C_r = ^{20}C_{r-10}$, then the value of $^{18}C_r$ is:

Given $^{ 20 }{ C }_{ r }=^{ 20 }{ C }_{ r-10 }$

We Know

$^{ n }{ C }_{ r }=^{ n }{ C }_{ n-r }\\ \Rightarrow r+(n-r)=n\\ \Rightarrow r+r-10=20\\ \Rightarrow 2r=30\\ \Rightarrow r=15\\ \Rightarrow ^{ 18 }{ C }_{ r }=^{ 18 }{ C }_{ 15 }\\ \Rightarrow \dfrac { 18! }{ 15!\times 3! } \\ \Rightarrow \dfrac { 18\times 17\times 16 }{ 3\times 2\times 1 } \\ \Rightarrow 48\times 17\\ \Rightarrow 816$

Hence the correct answer is $816$