Question

If ${}^{n-1}{C}_7{+}^{n-1}{C}_6>{}^n{C}_6$ then

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

Answer 1

The correct option is D $n>13$

Now,

${}^{n-1}{C}_7{+}^{n-1}{C}_6>{}^n{C}_6$

or, ${}^{n-1}{C}_7{+}^{n-1}{C}_{7-1}>{}^n{C}_6$

or, ${}^n{C}_7>{}^n{C}_6$

or, $\frac{n!}{7!(n-7)!}>\frac{n!}{6!(n-6)!}$

or, $n-6>7$

or, $n>13$.