Question

Com base nas letras da palavra MARCILEI determine:

a) quantos anagramas podem ser formados;

b) quantos anagramas começam com MAR (nessa ordem);

c) quantos anagramas começam e terminam com vogais;

d) quantos anagramas tem as consoantes juntas.​

Answer 1

a)

$\mathsf{P_8^2=\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot\diagup\!\!\!\!2!}{\diagup\!\!\!\!2!}=20160}$

b)

$\mathsf{\underbrace{\boxed{MAR}{CILEI}}_{P_6}}\\\mathsf{P_6=6!=6\cdot5\cdot4\cdot3\cdot2\cdot1=720}$

c)

$\mathsf{\underbrace{\boxed{II}}_{P_2^2}\underbrace{MRCL} _{P_4}\underbrace{\boxed{AE}}_{P2}}\\\mathsf{\dfrac{2!}{2!}\cdot4!\cdot2!=120\cdot2=240}$

anagramas em que as letras i não estão juntas:

$\mathsf{\underbrace{\boxed{IA}} _{P_2}\underbrace{MCLR}_{P_4}\underbrace{\boxed{EI}}_{P_2}}\\\mathsf{2!\cdot4!\cdot2!=96}$

$\mathsf{240+96=336}$

d)

$\mathsf{\underbrace{\boxed{MRCL}AIEI} _{P_5^2\cdot P_4}}\\\mathsf{\dfrac{5!}{2!}\cdot4!=1440}$

$\dotfill$

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