Question

um anagrama formado pela palavra Pernambuco é escolhido ao acaso. qual a probabilidade de começar com vogal?​

Answer 1

$\sf{\underbrace{PERNAMBUCO}_{P_{10}}=10!}\\\sf{n(U)=10!}\\\rm{Anagramas~comec_{\!\!,}ando~por~vogal:}\\\sf{\underbrace{\boxed{E}PRNAMBUCO}_{4\cdot P_9}=4\cdot9!}\\\sf{n(A)=4\cdot9!}$

$\sf{P(A)=\dfrac{n(A)}{n(U)}}\\\sf{P(A)=\dfrac{4\cdot9!}{10!}=\dfrac{4\cdot\diagdown\!\!\!\!9!}{10\cdot\diagdown\!\!\!\!9!}}\\\sf{P(A)=\dfrac{4\div2}{10\div2}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{P(A)=\dfrac{2}{5}}}}}}$