If ^15 C_ 3r = ^15 C_ r+3 , Find r. - Vidyadip

Question

If ${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$ Find r.

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Answer

We have, If ${ }^n C_p={ }^n C_q=n$ Then $p+q=n$ Also, ${ }^{15} C_{3 r}={ }^{15} C_{r+3}, \Rightarrow 3 r+r+3=154 r+3=154 r=15-34 r=12 r$ $=3$

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