Question

Quantos anagramas tem a palavra ARITMÉTICA?

Answer 1

Quantos anagramas tem a palavra ARITMÉTICA?

$P10^{2,2,2,1,1,1,1} =\dfrac{10!}{2!2!2!} =\dfrac{10!}{2!2.1.2.1} =\dfrac{10*9*8*7*6*5*[4]*3*(2!)}{2!2.1.2.1} = 453600~~anagramas$


Resposta : 453600 anagramas

Answer 2

$\mathsf{\underbrace{ARITMETICA}_{P_{10}^{2,2,2}}=\dfrac{10!}{2!\cdot2!\cdot2!}}\\\mathsf{\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot \diagup\!\!\!\!4\cdot3\cdot \diagup\!\!\!\!2!}{\diagup\!\!\!\!2!\cdot \diagup\!\!\!\!4}=453600}$