Question

Número de anagramas da palavras "ornitorrinco" ?

Answer 1

Anagramas: total de letras! / quantidade de letras que se repete!
o = 3 vezes
r = 3 vezes
i = 2 vezes
n = 2 vezes
$\frac{12!}{3! * 3! * 2! * 2!} = \frac{12*11*10*9*8*7*6*5*4*3*2}{3*2*3*2*2*2} =$ = 4*11*5*3*4*7*3*5*2*3*2 = 3 326 400

Answer 2

$\large \boxed{ \begin{array}{l} \underbrace{ \rm{ornitorrinco}} \\ \rm \: \: \: \: \: \: \: \: \: \: P_{12} {}^{3,3,2,2} \\ \\ \rm P_{12} {}^{3,3,2,2} = \dfrac{12!}{3! \times3 ! \times 2! \times 2!} \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times \cancel{ 3!}}{ \cancel{3!} \times 3! \times 2! \times 2!} \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 }{3! \times 2! \times 2! } \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{798 \cancel{33}600}{ \cancel{6} \times 2! \times 2! } \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{13305600}{2! \times 2! } \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{133 \cancel{05}600}{ \cancel{2} \times 2! } \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{665{2}800}{ 2! } \\ \\ \rm \: P_{12} {}^{3,3,2,2} = \dfrac{665 \cancel{2}800}{ \cancel{2}} \\ \\ \boxed{ \rm P_{12} {}^{3,3,2,2} =\boxed{3326400\rm\:anagramas }} \end{array}}$