Question

Com 9 vitaminas diferentes, quantos coquetéis de quatro ou mais vitaminas podemos formar?​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{C_{n,p} = \dfrac{n!}{p!(n- p)!}}$

$\mathsf{C_{9,4} + C_{9,5} + C_{9,6} + C_{9,7} + C_{9,8} + C_{9,9}}$

$\mathsf{\dfrac{9!}{4!.(9 - 4)!} + \dfrac{9!}{5!.(9 - 5)!} + \dfrac{9!}{6!.(9 - 6)!} + \dfrac{9!}{7!.(9 - 7)!} + \dfrac{9!}{8!.(9 - 8)!} + \dfrac{9!}{9!.(9 - 9)!}}$

$\mathsf{\dfrac{9!}{4!.5!} + \dfrac{9!}{5!.4!} + \dfrac{9!}{6!.3!} + \dfrac{9!}{7!.2!} + \dfrac{9!}{8!.1!} + \dfrac{9!}{9!.0!}}$

$\mathsf{\dfrac{9.8.7.6.5!}{4!.5!} + \dfrac{9.8.7.6.5!}{5!.4!} + \dfrac{9.8.7.6!}{6!.3!} + \dfrac{9.8.7!}{7!.2!} + \dfrac{9.8!}{8!.1!} + \dfrac{9!}{9!.0!}}$

$\mathsf{\dfrac{9.8.7.6}{4.3.2.1} + \dfrac{9.8.7.6}{4.3.2.1} + \dfrac{9.8.7}{3.2.1} + \dfrac{9.8}{2.1} + \dfrac{9}{1} + \dfrac{1}{1}}$

$\mathsf{126 + 126 + 84 + 36 + 9 + 1}$

$\boxed{\boxed{\mathsf{382}}}\leftarrow\textsf{letra E}$