Question

The value of $k$ is if ${}^6{\text{C}}_k=\frac{6!}{\left(4\right)!\times k!}$

• A. $5$
• B. $2$
• C. $4$
• D. $3$

Answer 1

The correct option is B $2$

Given that : ${}^6{\text{C}}_{=}\frac{6!}{4!\times k!}$
Since,
${}^6{\text{C}}_k=\frac{6!}{(6-k)!\times k!}$
Hence,
$\frac{6!}{(6-k)!\times k!}=\frac{6!}{4!\times k!}$
So,
$(6-k)!=4!$
$6-k=4$
$\Rightarrow k=2$