Question

6.4. Quantos anagramas são possíveis das palavras abaixo: a) Pera b) Banana c) Perfuma d) Habilida

Answer 1

Resposta:

Oi boa noite a resposta esta em cima

Answer 2

a)

$\mathsf{\underbrace{PERA}_{P_4}=4!=24}$

b)

$\mathsf{\underbrace{BANANA}_{P_6^{3,2}}=\dfrac{6!}{3!\cdot2!}}\\\mathsf{\dfrac{6\cdot5\cdot \diagup\!\!\!\!4\cdot \diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot \diagup\!\!\!\!2}=60}$

c)

$\mathsf{\underbrace{PERFUMA}_{P_7}=7!=5040}$

d)

$\mathsf{\underbrace{HABILIDA}_{P_8^{2,2}}=\dfrac{8!}{2!\cdot2!}} \\\mathsf{\dfrac{8\cdot7\cdot6\cdot5\cdot \diagup\!\!\!\!4\cdot3\cdot\diagup\!\!\!\!2!}{\diagup\!\!\!\!2!\cdot \diagup\!\!\!\!2}=10080}$

$\dotfill$

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