Question

Calcule:

Cn,4 = 4Cn,3​

Answer 1

Resposta:

$n =19$

Explicação passo a passo:

$C_{n,4} = {n \choose 4} = \frac{n!}{4!(n-4)!} = \frac{n \cdot (n-1) \cdot (n-2) \cdot (n-3) \cdot (n-4)!}{4! \cdot (n-4)!} = \frac{n \cdot (n-1) \cdot (n-2) \cdot (n-3)}{24}$

$C_{n,3} = {n \choose 3} = \frac{n!}{3!(n-3)!} = \frac{n \cdot (n-1) \cdot (n-2) \cdot (n-3)!}{3! \cdot (n-3)!} = \frac{n \cdot (n-1) \cdot (n-2)}{6}}$

Daí:

$\frac{n \cdot (n-1) \cdot (n-2) \cdot (n-3)}{24} = 4 \cdot \frac{n \cdot (n-1) \cdot (n-2)}{6}}$

Desenvolvendo:

$\frac{(n-3)}{24} = \frac{4}{6} \Leftrightarrow n-3 = 16 \Leftrightarrow n =19$