Question

tìm số tự nhiên n thỏa mãn: \(C^5_{n+5}=5A^3_{n+3}\)

Answer 1

\(\Leftrightarrow\dfrac{\left(n+5\right)!}{5!.n!}=\dfrac{\left(n+3\right)!.5}{n!}\)

\(\Leftrightarrow\left(n+5\right)\left(n+4\right)=5!.5=600\)

\(\Leftrightarrow n^2+9n-580=0\Rightarrow n=20\)