Question

If ${}^{15}C_{3r}={}^{15}C_{r+3}$ then the value of $r$ is

• A. $3$
• B. $4$
• C. $5$
• D. $8$

Answer 1

The correct option is A

$3$

Given: ${}^{15}C_{3r}={}^{15}C_{r+3}$

We know that, If ${}^{n}C_a={}^{n}C_b$Then $a+b=n\mathrm{or}\mathrm{a}=\mathrm{b}$

$\Rightarrow$$3r+r+3=15$

$\Rightarrow$ $r=3$

Hence, correct answer is option $\left(A\right)$.