Question

Quantos anagramas tem a palavra MATEMÁTICA?

Answer 1

$\boxed{\sf P_n^{a,b,c}=\dfrac{n!}{a!\cdot b!\cdot c!}}$

$\sf\underbrace{\sf MATEM\acute{A}TICA}_{\sf P_{10}^{2,3,2}}=\dfrac{10!}{2!\cdot3!\cdot2!}$

$\sf P_{10}^{2,3,2}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot1\cdot3\cdot2\cdot1\cdot2\cdot1}$

$\sf P_{10}^{2,3,2}=\dfrac{3628800}{24}$

$\boxed{\boxed{\sf P_{10}^{2,3,2}=151200}}$