Find $r$ if $^{15} C_{3 r} =^{15} C_{r + 3}$

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Solution

$^{15} C_{3 r} =^{15} C_{r + 3}$
$15 = 3 r + r + 3$ since $^{n} C_{x} =^{n} C_{y} \Rightarrow x = y$ or $n = x + y$
$\Rightarrow 15 = 4 r + 3$
$\Rightarrow 4 r = 12$
$∴ r = \frac{12}{4} = 3$

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Find $r$ if $^{15} C_{3 r} =^{15} C_{r + 3}$

If $^{15} C_{3 r} =^{15} C_{r + 3},$ find r.

^{15} C_{3 r} =^{15} C_{r + 3}

^{15} C_{3 r} :^{15} C_{r + 1} = 11 : 3

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^{15} C_{3 r} =^{15} C_{r + 3}

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