Question

quantos anagramas tem a palavra mississipi?

Answer 1

Temos 10 letras ....com repetições I(4) S(4)

Donde o número (N) de anagramas será dado por:

N = 10!/4!4! = 10.9.8.7.6.5.4!/4!4!

N = 10!/4!4! = 10.9.8.7.6.5/4!

N = 10!/4!4! = 10.9.8.7.6.5/4.3.2.1

N = 10!/4!4! = 151200/24

N = 10!/4!4! = 6300 <------ Número de anagramas

Espero ter ajudado

Answer 2

$\large\boxed{\begin{array}{l}\sf \underbrace{\sf MISSISSIPI}_{\sf P_{10}^{4,4}}=\dfrac{10!}{4!\cdot4!}\\\sf P_{10}^{4,4}=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot\diagdown\!\!\!\!\!4!}{\diagdown\!\!\!\!\!4!\cdot 4!}\\\sf P_{10}^{4,4}=\dfrac{10\cdot9\cdot\backslash\!\!\!4\cdot2\cdot7\cdot\backslash\!\!\!2\cdot\backslash\!\!\!3\cdot5}{\backslash\!\!\!4\cdot\backslash\!\!\!3\cdot\backslash\!\!\!2\cdot1}\\\sf P_{10}^{4,4}=6300~anagramas\end{array}}$