Question

1) Calcule o valor de:

a) A₈,₆

b) A₁₂,₃

c) A₁₀,₅

d) A₂₀,₁₈




2) De quantos modos podem ser escolhidos o presidente e o vice-presidente de UMA empresa entre 8 sócios?




3) Calcule o valor de:

a) C₆,₂

b) C₄,₂

c) C₉,₅

d) C₈,₄




4)Quantas comissões de 4 pessoas podem ser formadas com 10 pessoas?




5) Quantos times distintos de futebol de salão (5 jogadores) podem ser formados com 12 pessoas?

Answer 1

$\boxed{\begin{array}{l}\rm 1)\\\tt a)~\sf A_{8.6}=8\cdot7\cdot6\cdot5\cdot4\cdot2=20160\\\tt b)~\sf A_{12,3}=12\cdot11\cdot10\\\sf A_{12,3}=1320\\\tt c)~\sf A_{10,5}=10\cdot9\cdot8\cdot7\cdot6=30240\\\tt d)~\sf A_{20,18}=\dfrac{20!}{(20-18)!}\\\sf A_{20,18}=\dfrac{20!}{2!}~vou~deixar~indicado.\end{array}}$

$\boxed{\begin{array}{l}\rm 2)\\\sf \underline{8}\cdot\underline{7}=56~modos\\\rm 3)\\\tt a)~\sf C_{6,2}=\dfrac{6\cdot5}{2!}=\dfrac{30}{2}=15\\\tt b)~\sf C_{4,2}=\dfrac{4\cdot3}{2!}=\dfrac{12}{2}=6\\\tt c)~\sf C_{9,5}=\dfrac{9\cdot8\cdot7\cdot6\cdot5}{5!}=\dfrac{9\cdot\diagup\!\!\!8^2\cdot7\cdot\diagup\!\!\!6\cdot\diagup\!\!\!5}{\diagup\!\!\!5\cdot\diagup\!\!\!4_1\cdot\diagup\!\!\!3\cdot\diagup\!\!\!2\cdot1}\\\sf C_{9,5}=9\cdot2\cdot7=126\end{array}}$

$\boxed{\begin{array}{l}\tt d)~\sf C_{8,4}=\dfrac{8\cdot7\cdot6\cdot5}{4!}=\dfrac{\diagup\!\!\!8^2\cdot7\cdot\diagup\!\!\!6\cdot5}{\diagup\!\!\!4_1\cdot\diagup\!\!\!3\cdot\diagup\!\!\!2\cdot1}\\\sf C_{8,4}=2\cdot7\cdot5=70\end{array}}$

$\boxed{\begin{array}{l}\rm 4)~\sf C_{10,4}=\dfrac{10\cdot\diagup\!\!\!9^3\cdot\diagup\!\!\!8\cdot7}{\diagup\!\!\!4\cdot\diagup\!\!\!3_1\cdot\diagup\!\!\!2\cdot1}\\\sf C_{10,4}=10\cdot3\cdot7=210~comiss\tilde oes\\\rm 5)~\sf C_{12,5}=\dfrac{\diagdown\!\!\!\!\!\!12\cdot11\cdot\diagdown\!\!\!\!\!\!10\cdot9\cdot8}{\diagdown\!\!\!5\cdot\diagdown\!\!\!\!4\cdot\diagdown\!\!\!\!3\cdot\diagdown\!\!\!2\cdot1}\\\sf C_{12,5}=11\cdot9\cdot8\\\sf C_{12,5}=792~times\end{array}}$