Question

What is the value of $r$ when ${}^{20}{C}_r$ has its greatest value?

• A. $0$
• B. $20$
• C. $10$
• D. $1$

Answer 1

The correct option is C $10$

Maximum value of ${}^n{C}_r$ is at ${}^n{C}_{\frac{n}{2}}$ ..... (when $n$ is even)

$\Rightarrow r=\frac{n}{2}$

In ${}^{20}{C}_r,$ $n=20$

$\Rightarrow$ Maximum value of ${}^{20}{C}_r$ is at $r=\frac{n}{2}$

$\Rightarrow r=\frac{20}{2}=10$

Therefore $r=10$