Question

Quais os resultados para a resolução dos números binomiais abaixo

Answer 1

Explicação passo-a-passo:

• $\sf \dbinom{9}{3}=\dfrac{9!}{3!\cdot(9-3)!}$

$\sf \dbinom{9}{3}=\dfrac{9!}{3!\cdot6!}$

$\sf \dbinom{9}{3}=\dfrac{9\cdot8\cdot7\cdot6!}{3!\cdot6!}$

$\sf \dbinom{9}{3}=\dfrac{9\cdot8\cdot7}{3!}$

$\sf \dbinom{9}{3}=\dfrac{504}{6}$

$\sf \dbinom{9}{3}=84$

• $\sf \dbinom{9}{6}=\dfrac{9!}{6!\cdot(9-6)!}$

$\sf \dbinom{9}{6}=\dfrac{9!}{6!\cdot3!}$

$\sf \dbinom{9}{6}=\dfrac{9\cdot8\cdot7\cdot6!}{6!\cdot3!}$

$\sf \dbinom{9}{6}=\dfrac{9\cdot8\cdot7}{3!}$

$\sf \dbinom{9}{6}=\dfrac{504}{6}$

$\sf \dbinom{9}{6}=84$

Logo, $\sf \dbinom{9}{3}=\dbinom{9}{6}$