Question

Quantos são os anagramas da palavra ALGEBRA? Quantos desses anagramas começam com a letra A?

Answer 1

$\large\boxed{\begin{array}{l}\sf A\,palavra\,ALGEBRA\,possui\,7\,letras.\\\sf das\,quais\,duas\,se\,repetem.\\\sf o\,n\acute umero\,de\,anagramas\,\acute e\\\sf P_7^2=\dfrac{7!}{2!}=\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot\diagdown\!\!\!\!\!2!}{\diagdown\!\!\!\!\!2!}=2520\,anagramas.\end{array}}$

$\large\boxed{\begin{array}{l}\sf Comec_{\!\!,}ando\,pela\,letra\,A\\\sf temos\,6\,letras\,para\,permutar.\\\sf P_6=6!=6\cdot5\cdot4\cdot3\cdot2\cdot1=720\,anagramas.\end{array}}$