Question

If ${{}^{n}C}_8={{}^{n}C}_5$, then the value of $n$ is

• A. $2$
• B. $3$
• C. $1$
• D. $13$

Answer 1

Answer: (D)

$13$

Given, ${{}^{n}C}_8={{}^{n}C}_5$.

We have the formula for combination,

${}^n{C}_r={}^n{C}_{(n-r)}$

$⟹$ $n-r=5$, if $r=8$ OR

$n-r=8$, if $r=5$

$⟹$ $n-8=5$ OR $n-5=8$

From both the equations we get $n=13$.

Hence, option $D$ is correct.