Question

9) O total de anagramas da palavra GEOGEBRA é igual a
A) P 2/9
B) P 8/2
C) P 2,2/8
D)P 4/8
E)P 8.

Answer 1

Vamos lá, a palavra GEOGEBRA tem 8 letras e G e E se repetem duas vezes, logo:

$\Large\displaystyle\begin{gathered} \sf P_8^{2,2}=\frac{8!}{2!\cdot 2!} =\frac{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot \backslash\!\!\!2}{\backslash\!\!\!2\cdot 2} \end{gathered}$

$\Large\displaystyle\begin{gathered} \sf P_8^{2,2}=\frac{20160}{ 2} \end{gathered}$

$\Large\displaystyle\text{ \begin{gathered} \boxed{\sf P_8^{2,2}=10080\ anagramas.}\end{gathered} }$

Veja mais sobre:

• brainly.com.br/tarefa/32645669

Answer 2

$\large \boxed{ \begin{array}{l} \underbrace{ \sf{GEOGEBRA}} \\ \: \: \: \: \: \: \: \: \: \: \sf{P^{2 ,2}_8} \\ \\ \sf{\sf{P^{2 ,2}_8} = \dfrac{8!}{2! \: . \: 2!} } \\ \\ \sf{P^{2 ,2}_8} = \dfrac{8 \: . \: 7 \: . \: 6 \: . \: 5 \:. \: 4 \: . \: 3 \: . \: 2 \: . \: 1}{2 \: . \: 2} \\ \\ \sf{P^{2 ,2}_8} = \dfrac{40320}{4} \\ \\ \boxed{\sf{P^{2 ,2}_8} = 10080 \:anagramas } \checkmark\end{array}}$