Question

Na palavra MATEMATICA, quantos anagramas podem ser formados?


A) 800
B) 1680
C) 3455
D) 2000
E) 1300​

Answer 1

$\green{\boxed{\begin{array}{l}\sf\underbrace{\sf MATEMATICA}_{P_{10}^{2,2,3}}=\dfrac{10!}{2!\cdot2!\cdot3!}\\\sf P_{10}^{2,2,3}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot\diagdown\!\!\!\!4\cdot\diagdown\!\!\!\!\!3!}{\diagdown\!\!\!\!2\cdot\diagdown\!\!\!\!2\cdot\diagdown\!\!\!\!3!}\\\sf P_{10}^{2,2,3}=151200~anagramas.\\\sf corrija~o~gabarito\blue{\checkmark}\end{array}}}$