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

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Solution

If $^{n} C_{p} =^{n} C_{q}$

Then p + q = n

$\Rightarrow^{15} C_{3 r} =^{15} C_{r + 3},$

$\Rightarrow 3 r + r + 3 = 15$

$4 r + 3 = 15$

$4 r = 15 - 3 = 12$

$r = 3$

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Similar questions

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

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

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

r

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

r

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

r

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