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

(A) 3

(B) 4

(C) 5

(D) 8

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Best answer

**SOLUTION —**

$\begin{array}{l}{ }^{13} \mathrm{C}_{3 n}={ }^{15} \mathrm{C}_{r+3} \\\Rightarrow \quad 3 r=r+3 \text { or } 15-3 r=r+3 \\\Rightarrow \quad r=\frac{3}{2} \text { or } r=3 \\\therefore \quad r=3 \quad(\because r \text { is positive integer) } \\\end{array}$

So, The correct option will be **(A).**

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