Question

If ${}^n{C}_5={}^n{C}_{10}$, then the value of ${}^{16}{C}_n$ is

• A. $560$
• B. $1$
• C. $120$
• D. $16$

Answer 1

The correct option is D $16$

Given
${}^n{C}_5={}^n{C}_{10}$
We know that,
${}^n{C}_r={}^n{C}_{n-r}$
So,
${}^n{C}_{10}={}^n{C}_{n-5}\Rightarrow n-5=10\Rightarrow n=15\Rightarrow {}^{16}{C}_{15}=16$