Question

8- Quantos anagramas têm as palavras:
a) PATA

b) GUANABARA


9- Considerando a palavra PANTANAL:
a) quantos anagramas podemos formar?

b) quantos anagramas começam pela letra A?

Answer 1

Resposta:

$\text{Leia abaixo}$

Explicação passo-a-passo:

8.

$a)\:P_4^2 = \dfrac{4!}{2!} = \dfrac{4.3.2!}{2!} = 12$

$b)\:P_9^4 = \dfrac{9!}{4!} = \dfrac{9.8.7.6.5.4!}{4!} = 15.120$

9.

$a)\:P_8^{3,2} = \dfrac{8!}{3!2!} = \dfrac{8.7.6.5.4.3!}{3!2!} = 3.360$

$b)\:P_7^{2,2} = \dfrac{7!}{2!2!} = \dfrac{7.6.5.4.3.2!}{2!2!} = 1.260$

Answer 2

8)

a)

$\mathsf{\underbrace{PATA}_{P_4^2}=\dfrac{4!}{2!}=\dfrac{4\cdot3\cdot\diagup\!\!\!\!2!}{\diagup\!\!\!\!2!}=12}$

b)

$\mathsf{\underbrace{GUANABARA}_{P_9^4}=\dfrac{9!}{4!}}\\\mathsf{\dfrac{9\cdot8\cdot7\cdot6\cdot5\cdot\diagup\!\!\!\!4!}{\diagup\!\!\!\!4!}=15120}$

9)

a)

$\mathsf{\underbrace{PANTANAL}_{P_8^{3,2}}=\dfrac{8!}{3!\cdot2!}}\\\mathsf{\dfrac{8\cdot7\cdot6\cdot5\cdot\diagup\!\!\!\!4\cdot\diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot\diagup\!\!\!\!4}=3360}$

b)

$\mathsf{\boxed{A}\underbrace{PNTANAL}_{P_7^{2,2}}=\dfrac{7!}{2!\cdot2!}}\\\mathsf{\dfrac{7\cdot6\cdot5\cdot\diagup\!\!\!\! 4\cdot3\cdot \diagup\!\!\!\! 2!}{\diagup\!\!\!\!2!\cdot \diagup\!\!\!\!2}=1260}$