Question

Find n, if $\rm ^{18}C_{3n} =\ \rm ^{18}C_{2n+3}$

Answer 1

Solution :

Given

$\rm ^{18}C_{3n} =\ \rm ^{18}C_{2n+3}$

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We know that ,

If $\rm ^{n}C_{r} =\ \rm ^{n}C_{p}$

then either r = p or

r + p = n

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Here ,

r = 3n , p = 2n + 3

r = p

=> 3n = 2n + 3

=> 3n - 2n = 3

=> n = 3

Therefore ,

n = 3

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