Question

Determine o número de anagramas das palavras: “M A T E M A T I C A” e “ P Á S S A R O S” e por
fim, calcule o quociente dos números dos anagramas, respectivamente.

a)100
b)80
c)70
d)40
e)90​

Answer 1

$\mathsf{\underbrace{MATEMATICA}_{P_{10}^{3,2,2}}=\dfrac{10!}{3!\cdot2!\cdot2!}}\\\mathsf{\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot\diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot4}=302400}$

$\mathsf{\underbrace{PASSAROS}_{P_8^{3,2}}=\dfrac{8!}{3!\cdot2!}}\\\mathsf{\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot \diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot2}=3360}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\dfrac{302400}{3360}=90}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\maltese~~alternativa~~e}}}}}$

$\dotfill$

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