Question

$\large\begin{array}{lr}\sf{Uma\,senha\,n{\'u}mera\,ser{\'a}\,formada\,por\,4\,d{\'i}gitos}\\\sf{destintos,entre\,os\,d{\'i}gitos\,0,\!1,\!2,\!3,\!4,\!5,\!6,\!7,\!8,\!9}\\\sf quantas\,formas\,diferentes\,a\,senha\,poder{\'a}\,ser\\\sf{formada?}\end{array}$​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\textsf{Neste caso, a ordem dos n{\'u}meros {\'e} relevante, trata-se de arranjo:}$

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

$\mathsf{A_{\:10,4} = \dfrac{10!}{(10 - 4)!}}$

$\mathsf{A_{\:10,4} = \dfrac{10.9.8.7.\not6!}{\not6!}}$

$\boxed{\boxed{\mathsf{A_{\:10,4} = 5.040}}}\leftarrow\textsf{senhas diferentes}$

Answer 2

$A _{n \: , \: p} = \frac{n!}{(n - p)!} \\ A _{10 \: , \: 4} = \frac{10!}{(10 - 4)!} \\ A _{10 \: ,\: 4} = \frac{10 \: . \: 9 \: . \: 8 \: . \: 7 \: . \: 6!}{6!} \\ A _{10 \: , \: 4} = 10 \: . \: 9 \: . \: 8 \: . \: 7 \\ \boxed{\boxed{\boxed{A_{10 \: ,\: 4} = 5 \: 040 }}}$

att. yrz