Question

quantos anagramas podem ser formados pela palavra sociologia? quantos anagramas começam pela letra S e terminam com a letra A?

Answer 1

$\boxed{\begin{array}{l}\sf Anagramas~da~palavra~SOCIOLOGIA:\\\sf\underbrace{\sf SOCIOLOGIA}_{P_{10}^{3,2}}=\dfrac{10!}{3!\cdot2!}\\\sf P_{10}^{3,2}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot\diagdown\!\!\!4^2\cdot\diagdown\!\!\!\!\!3!}{\diagdown\!\!\!\!\!3!\cdot\diagdown\!\!\!2\cdot1}\\\sf P_{10}^{3,2}=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot2\\\sf P_{10}^{3,2}=302400~anagramas\end{array}}$

$\boxed{\begin{array}{l}\sf Anagramas~da~palavra~que~comec_{\!\!,}am~pela~letra~S\\\sf e~terminam~com~a~letra~A:\\\sf\underbrace{\sf\boxed{\sf S}OCIOLOGI\boxed{\sf A}}_{P_8^{3,2}}=\dfrac{8!}{3!\cdot2!}\\\sf P_8^{3.2}=\dfrac{8\cdot7\cdot6\cdot5\cdot\diagdown\!\!\!4^2\cdot\diagdown\!\!\!\!\!3!}{\diagdown\!\!\!\!\!3!\cdot\diagdown\!\!\!2}\\\sf P_8^{3,2}=8\cdot7\cdot6\cdot5\cdot2\\\sf P_8^{3,2}=3360~anagramas \end{array}}$