Question

Determine o valor de n nas equacoes abaixo a)Cn,12=C30,18 resposta30
b)C14,3=Cn,11 resposta14

Answer 1

a)
C(n,12) = C(30,18)
n!                =      30!           
12!(n - 12)!      18!(30 - 18)!
$\frac{n!}{(n - 12)!} = \frac{30!12!}{18!12!} \\ \frac{n!}{(n - 12)!} = \frac{30!}{18!}$
Podemos "cortar" os fatoriais.
$\frac{n}{n - 12} = \frac{30}{18} \\ n = 30$

b)
C(n,11) = C(14,3)
$\frac{n!}{11!(n -11)!} = \frac{14!}{3!(14 - 3)!} \\ \frac{n!}{(n - 11)!} = \frac{14!11!}{3!11!} \\ \frac{n!}{(n - 11)!} = \frac{14!}{3!}$
"Cortando os fatoriais:
$\frac{n}{n - 11} = \frac{14}{3} \\ n = 14$