Question

quantos anagramas podem ser formados com a palavra MATEMATICA
*permutação com repetição*

a) 300.005
b) 302.000
c) 302.400
e) 364.000​

Answer 1

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$\sf{\underbrace{MATEM\acute{A}TICA}_{P_{10}^{3,2}}=\dfrac{10!}{3!\cdot2!}}\\\sf{P_{10}^{3,2}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot\diagup\!\!\!4^2\cdot\diagdown\!\!\!\!\!\!3!}{\diagdown\!\!\!\!\!\!3!\cdot\diagup\!\!\!2}}\\\sf{P_{10}^{3,2}=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot2}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf{P_{10}^{3,2}=302400}}}}}}\\\Huge\boxed{\boxed{\boxed{\boxed{\boxed{\tt{\maltese~alternativa~~c}}}}}}$