Question

quantos anagramas podem ser formados pela palavra topologia? quantos anagramas começam pela letra G e terminam com a letra O?

Answer 1

$\boxed{\begin{array}{l}\sf Anagramas~da~palavra~TOPOLOGIA:\\\sf\underbrace{\sf TOPOLOGIA}_{P_9^3}=\dfrac{9!}{3!}\\\sf P_9^3=\dfrac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot\diagdown\!\!\!\!\!3!}{\diagdown\!\!\!\!\!3!}\\\sf P_9^3=60480~anagramas\end{array}}$

$\boxed{\begin{array}{l}\sf Anagramas~da~palavra~TOPOLOGIA~que~comec_{\!\!,}am\\\sf pela~letra~G~e~terminam~com~a~letra~O:\\\sf\underbrace{\sf\boxed{\sf G}TOPOLIA\boxed{\sf O}}_{ P_7^2}=\dfrac{7!}{2!}\\\sf P_7^2=\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot\diagdown\!\!\!\!\!2!}{\diagdown\!\!\!\!\!\!2!}\\\sf P_7^2=2520~anagramas\end{array}}$