If $^{49} C_{3 r - 2} =^{49} C_{2 r + 1}$ find $^{'} r^{'}$

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Solution

$^{n} C_{r} =^{n} C_{3}$ if either $r = s$ or $r + s = n$
Thus, $3 r - 2 = 2 r + 1$
$\Rightarrow r = 3$

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