Correct Answer - Option 3 : 5
Concept:
The number of all combinations of n distinct things taken r at a time (r ≤ n) is:
\(^{n}C_{r}=\frac{n!}{(n-r)!r!}\)
Calculation:
Since 2nC3 : nC2 = 12 : 1
\(⇒ \frac{2n!}{(2n-3)!\space 3!}:\frac{n!}{(n-2)!\space 2!}=12:1\)
\(⇒ \frac{2n(2n-1)(2n-2)}{3\times 2\times 1}:\frac{n(n-1)}{2\times 1}=12:1\)
⇒ 2n - 1 = 9
⇒ n = 5
