Question

Quantas comissões de 6 elementos podemos formar com 30 alunos de uma turma?

Answer 1

Resposta:

$C(30,6)=\frac{30!}{6!(30-6)!} \\ \\ C(30,6)=\frac{30!}{6!.24!}\\ \\ C(30,6)=\frac{30.29.28.27.26.25.24!}{6!.24!}\\ \\ C(30,6)=\frac{30.29.28.27.26.25}{6.5.4.3.2.1}$

$C(30,6)=\frac{427518000}{720}\\ \\ C(30,6)=593775$

593775 comissões.

bons estudos!

Answer 2

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\Large\boxed{\begin{array}{l} \Large\boxed{\begin{array}{l} \sf{C_{n,p} = \dfrac{n!}{p!(n - p)!} }\end{array}}\end{array}}\rightarrow\Large\boxed{\begin{array}{l} \Large\boxed{\begin{array}{l} \sf{n = 30 } \\ \sf{p = 6}\end{array}}\end{array}}$

$\Large\boxed{\begin{array}{l} \Large\boxed{\begin{array}{l} \sf{C_{30,6} = \dfrac{30!}{6!(30 - 6)!}} \\ \\ \sf{ C_{30,6} = \dfrac{30 \: . \: 29 \: . \: 28 \: . \: 27 \: . \: 26 \:. \: 25 \: . \: \not24!}{6! \: . \: \not24!} } \\ \\ \sf{ C_{30,6} = \dfrac{30 \: . \: 29 \: . \: 28 \: . \: 27 \: . \: 26 \: . \: 25}{6 \: . \: 5 \: . \: 4 \: . \: 3 \: .\: 2 \: . \: 1} } \\ \\ \sf{C_{30,6} = \dfrac{427518000}{720} } \\ \\ \boxed{\boxed{ \boxed{ \boxed{\sf{C_{30,6} =593775 }}}}} \Large\checkmark\end{array}}\end{array}}$