Question

If ${}^{20}{C}_r{=}^{20}{C}_{r-10}$, then the value of ${}^{18}{C}_r$ is:

• A. $4896$
• B. $5432$
• C. $816$
• D. $1632$

Answer 1

The correct option is C $816$

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

We Know

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

Hence the correct answer is $816$