Question

1 - Determine a quantidade de anagramas possiveis de cada palavra abaixo:
a) arara
b) atividade
c) jabuticaba
d) assessorio

Answer 1

a) 5! = 120

b) 9! = 362880

c) 10! = 3628800

d) 10! = 3628800

conta a quantidade de palavras. ex: arara tem 5 palavras, faz 5x4x3x2x1 = 120

isso é anagrama

Answer 2

a)

$\mathsf{\underbrace{ARARA}_{P_5^{3,2}}=\dfrac{5!}{3!\cdot2!}}\\\mathsf{\dfrac{5\cdot \diagup\!\!\!\! 4\cdot \diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot \diagup\!\!\!\!2}=10}$

b)

$\mathsf{\underbrace{ATIVIDADE}_{P_9^{2,2,2}}=\dfrac{9!}{2!\cdot2!\cdot2!}}\\\mathsf{\dfrac{9\cdot8\cdot7\cdot6\cdot5\cdot \diagup\!\!\!\!4\cdot3\cdot \diagup\!\!\!\!2!}{\diagup\!\!\!\!2!\cdot\diagup\!\!\!\!4}=45360}$

c)

$\mathsf{\underbrace{JABUTICABA}_{P_{10}^{3,2}}=\dfrac{10!}{3!\cdot2!}}\\\mathsf{\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot \diagup\!\!\!\!4\cdot \diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot\diagup\!\!\!\!2}=302400}$

d)

$\mathsf{\underbrace{ASSESSORIO}_{P_{10}^{4,2}}=\dfrac{10!}{4!\cdot2!}}\\\mathsf{\dfrac{10\cdot9\cdot8\cdot7\cdot \diagup\!\!\!\!6\cdot5\cdot \diagup\!\!\!\!4!}{\diagup\!\!\!\!4!\cdot \diagup\!\!\!\!6}=75600}$

$\dotfill$

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