Question

If $^{n-1}C_6+ \,{}^{n-1}C_7 > \,{}^nC_6 $, then

• A. $n > 4$
• B. $n > 12$
• C. $n \ge 13$
• D. $n > 13$

Answer 1

Answer: (D)

$^{n-1}C_{6} +\,{}^{n-1}C_{7}= \,{}^{n}C_{7}= \, \therefore ^{n}C_{7} >\,{}^{n}C_{6}$.
$\Rightarrow \frac{n\,!}{7\,!\, n-7\,!} > \frac{n\,!}{6\,!\,n-6\,!}$
$\Rightarrow \frac{1}{7.6\,!\,n-7\,!} > \frac{1}{6\,!\left(n-6\right)\left(n-7\right)\,!}$
$\Rightarrow n-6\,>\,7$
$\Rightarrow n\, >\,13$