If $^nC_9 = ^nC_8$, then the value of n is

Explanation

$$ ^nC_9 = ^nC_8 $$ $$ \frac{n!}{9!(n-9)!} = \frac{n!}{8!(n-8)!} \quad [\because ^nC_r = \frac{n!}{r!(n-r)!}] $$ $$ \frac{1}{9 \times 8! (n-9)!} = \frac{1}{8! \times (n-8) \times (n-9)!} $$ $$ (n-8) = 9 $$ $$ n = 9 + 8 $$ $$ n = 17 $$