A) 4
B) 6
C) 8
D) 7
Correct Answer: C
Solution :
Given, \[^{n-1}{{C}_{3}}{{+}^{n-1}}{{C}_{4}}{{>}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[^{n}{{C}_{4}}{{>}^{n}}{{C}_{3}}\] \[\Rightarrow \] \[\frac{n!}{(n-4)!4!}>\frac{n!}{(n-3)!3!}\] \[\Rightarrow \] \[\frac{n!}{4.3!(n-4)!}>\frac{1}{(n-3)(n-4)!3!}\] \[\Rightarrow \] \[\frac{1}{4}>\frac{1}{n-3}\] \[\Rightarrow \] \[n-3>4\] \[\Rightarrow \] \[n>7\] or \[n=8\]
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