Question

Calcule o número de anagramas da palavra ANTONIA. *

5 pontos

a) 1260

b) 1270

c) 1280

d) 1350

​

Answer 1

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$\boxed{\sf{\underline{Permutac_{\!\!,}\tilde{a}o~com~repetic_{\!\!,}\tilde{a}o}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf P_n^{\alpha,\beta,\gamma}=\dfrac{n!}{\alpha!\cdot\beta!\cdot\gamma!...}}}}}$

$\sf\underbrace{ANTONIA}_{P_7^{2,2}}=\dfrac{7!}{2!\cdot2!}\\\sf P_7^{2,2}=\dfrac{7\cdot6\cdot5\cdot\diagdown\!\!\!\!\!4^2\cdot3\cdot\diagdown\!\!\!\!2!}{\diagdown\!\!\!\!2!\cdot\diagdown\!\!\!\!2}\\\sf P_7^{2,2}=1260$