Question

9- Quantos são os anagramas da palavra BANANADA que:
A-começam com a letra B
B-terminam com a letra A
C-começam com B e terminam com A

Answer 1

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$\boxed{\begin{array}{l}\rm a)~\sf\underbrace{\sf\boxed{\sf B}ANANADA}_{\sf P_7^{2,4}}=\dfrac{7!}{2!\cdot4!}\\\sf P_7^{2,4}=\dfrac{7\cdot\diagup\!\!\!6^3\cdot5\cdot\diagup\!\!\!\!\!\!4!}{\diagup\!\!\!2^1\cdot1\cdot\diagup\!\!\!\!\!\!4!}=7\cdot3\cdot5=105~anagramas\\\rm b)~\sf\underbrace{\sf\boxed{\sf A}BNANADA}_{\sf P_7^{3,2}}=\dfrac{7!}{3!\cdot2!}\\\sf P_7^{3,2}=\dfrac{7\cdot6\cdot5\cdot\diagup\!\!\!4^2\cdot\diagup\!\!\!\!\!\!3!}{\diagup\!\!\!\!\!\!3!\cdot\diagup\!\!\!2\cdot1}=420~anagramas\end{array}}$

$\boxed{\begin{array}{l}\rm c)~\sf\underbrace{\sf \boxed{\sf B}ANANAD\boxed{\sf A}}_{\sf P_6^{3,2}}=\dfrac{6!}{3!\cdot2!}\\\sf P_6^{3,2}=\dfrac{6\cdot5\cdot\diagup\!\!\!4^2\cdot\diagup\!\!\!\!\!\!3!}{\diagup\!\!\!\!\!\!3!\diagup\!\!\!2\cdot1}\\\sf P_6^{3,2}=6\cdot5\cdot2=60~anagramas\end{array}}$