Question

A palavra POTÁSSIO possui quantos anagramas que começam e terminam com a mesma letra?

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm anagramas\,que\,iniciam\,e\,terminam}\\\underline{\rm por\,O:}\\\sf Teremos\,6\,letras\,com\,repetic_{\!\!,}\tilde ao\,de\,duas\\\sf para\,permutar.\\\sf P_6^2=\dfrac{6!}{2!}=\dfrac{6\cdot5\cdot4\cdot3\cdot\diagdown\!\!\!\!\!\!2!}{\diagdown\!\!\!\!\!\!2!}=360\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm anagramas\,que\,iniciam\,e\,terminam}\\\underline{\rm por\,S}\\\sf mesma\,an\acute alise\,do\,caso\,anterior.\\\sf P_6^2=\dfrac{6!}{2!}=360\\\sf Ao\,todo\,teremos\\\sf 360+360=720\,anagramas.\end{array}}$