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

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Solution

The correct option is A 3
Since, $^{n} C_{r} =^{n} C_{n - r}$
Either $⟹ 3 r = r + 3$ or $3 r = 15 - (r + 3)$
Hence, $r = \frac{3}{2}$ or $r = 3$
Since r is an integer, therefore $r = 3$

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