Question

If ${}^n{C}_3=220,$ then n equals to:

• A. 10
• B. 11
• C. 12
• D. 9
• E. 8

Answer 1

Answer: (C)

${}^n{C}_3=220$ $\Rightarrow$ $\frac{n!}{(n-3)!3!}=220$ $\Rightarrow$ $n(n-1)(n-2)=220\times 6$ $\Rightarrow$ $n(n-1)(n-2)=12(12-1)(12-2)$ $\Rightarrow$ $n=12$