Question

Quantos são os arranjos de 7 elementos, tomados 4 a 4?​

Answer 1

Resposta:

A(n ,p) = n! /(n-p)!

A(7, 4) = 7!/(7-4)!

A(7, 4) = 7!/(3)!

A(7, 4) = 7.6.5.4.3!/3!

A(7, 4) = 7.6.5.4

A(7, 4) = 840

Answer 2

✅ Após resolver os cálculos, concluímos que o total de arranjos simples de "9" elementos tomados "3" em "3" é:

       $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf A_{7,\:4} = 840\:\:\:}}\end{gathered} }$

Para calcularmos arranjos simples, devemos utilizar a seguinte fórmula:

         $\Large\displaystyle\begin{gathered}\tt A_{n,\:k} = \frac{n!}{(n - k)!}\end{gathered}$

Sendo os valores:

                $\Large\begin{cases}\tt n = 7\\\tt k = 4 \end{cases}$

Então, temos:

         $\Large\displaystyle\begin{gathered}\tt A_{7,\:4} = \frac{7!}{(7 - 4)!}\end{gathered}$

                    $\Large\displaystyle\begin{gathered}\tt = \frac{7!}{3!}\end{gathered}$

                    $\Large\displaystyle\text{ \begin{gathered}\tt = \frac{7\cdot6\cdot5\cdot4\cdot{\!\diagup\!\!\!\!\!3!}}{\!\diagup\!\!\!\!\!3!}\end{gathered} }$

                    $\Large\displaystyle\begin{gathered}\tt = 7\cdot6\cdot5\cdot4\end{gathered}$

                    $\Large\displaystyle\begin{gathered}\tt = 840\end{gathered}$

✅ Portanto, o total de arranjos é:

          $\Large\displaystyle\begin{gathered}\tt A_{7,\:4} = 840\end{gathered}$

Saiba mais:

1. https://brainly.com.br/tarefa/49323154
2. https://brainly.com.br/tarefa/35018185