Question

If ${}^n{\text{C}}_r=\frac{n!}{(n-r)!\times r!}$ then ${}_n{\text{C}}_r$ is

• A. $\frac{n!}{(n-r)!\times r!}$
• B. $\frac{(n-r)!\times r!}{n!}$
• C. $\frac{r!}{(n-r)!\times n!}$
• D. All of the above.

Answer 1

The correct option is A $\frac{n!}{(n-r)!\times r!}$

Since ${}^n{\text{C}}_r$ and ${}_n{\text{C}}_r$ are different notations for combination.
Hence,
${}^n{\text{C}}_r=$ ${}_n{\text{C}}_r$
$\Rightarrow$ ${}_n{\text{C}}_r=\frac{n!}{(n-r)!\times r!}$