Question

Quantos anagramas da palavra PIRACICABA terminam em vogal? Calcule.

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Anagramas\,que\,terminam\,por\,A}\\\\\sf P_9^{2,2,2}=\dfrac{9!}{2!\cdot 2!\cdot 2!}=\dfrac{9\cdot8\cdot7\cdot6\cdot5\cdot\backslash\!\!\!4\cdot3\cdot\diagdown\!\!\!\!\!2!}{\diagdown\!\!\!\!\!\!2!\cdot \backslash\!\!\!2\cdot\backslash\!\!\!2}\\\\\sf P_9^{2,2,2}=45360\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm Anagramas\,que\,terminam\,em\,I}\\\\\sf P_9^{3,2}=\dfrac{9!}{3!\cdot2!}=\dfrac{9\cdot8\cdot7\cdot6\cdot5\cdot\backslash\!\!\!4^2\cdot\diagdown\!\!\!\!\!3!}{\diagdown\!\!\!\!3!\cdot\backslash\!\!\!2}\\\\\sf P_{10}^{3,2}=30240\end{array}}$

$\large\boxed{\begin{array}{l}\sf o\,total\,\acute e\\\sf 45360+30240=75600\,anagramas\end{array}}$