Question

03. Considere os anagramas da palavra PIRATARIA. Quantos anagramas
apresentar as letras RAT juntas?
RAPIDO POR GENTILEZA!!​

Answer 1

$\large\boxed{\begin{array}{l}\sf\underbrace{\sf PI\boxed{\sf RAT} ARIA}_{ P_7^{2,2}\cdot P_3}=\dfrac{7!}{2!\cdot2!}\cdot 3!\\\sf P_7^{2,2}\cdot P_3=\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot\diagdown\!\!\!\!\!2!}{\diagdown\!\!\!\!\!2!\cdot\diagdown\!\!\!\!\!2!}\cdot3\cdot\diagdown\!\!\!\!\!2!\\\sf P_7^{2,2}\cdot P_3=7\cdot6\cdot5\cdot4\cdot3\cdot3\\\sf P_7^{2,2}\cdot P_3=7560\end{array}}$