Question

considerando os anagramas da palavra MATEMÁTICA,determine:
a) o número total de anagramas ​

Answer 1

Resposta:

$\text{Leia abaixo}$

Explicação passo-a-passo:

$\text{P}_{10}^{3,2,2} = \dfrac{10!}{3!.2!.2!} = \dfrac{10.9.8.7.6.5.4.3!}{3!.2!.2!} = 151.200$

Answer 2

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

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

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

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

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