Question

quantos anagramas tem a palavra fisioterapia

Answer 1

$\text{A palavra "fisioterapia" tem 12 letras, sendo que a letra "i" se}\\\text{apresenta 3 vezes e a letra "a", 2 vezes.}\\\text{Portanto, a quantidade de anagramas dessa palavra}\mathrm{\ ser\acute{a}\ dada\ por:}\\\\\dfrac{12!}{3!\times2!}\Longrightarrow\dfrac{12\times11\times10\times9\times8\times7\times6\times5\times4\ \times\!\!\not3!}{\not3!\times2}\Longrightarrow\dfrac{12\times11\times10\times9\times8\times7\times6\times5\times4}{2}\\\\\\\Longrightarrow12\times11\times10\times9\times8\times7\times6\times5\times2=\boxed{\boxed{39916800\ \text{anagramas}}}$

Answer 2

Pn=12!/3!2!/>Pn=12*11**10*9*8*7*6*5*4*3*2*1/3*2*1*2*1 Pn=479.001.600/12 PN=39.916.800