Question

Quantos são os anagramas das palavras abaixo?

a) CALADA

b) BOLO

c) VIVI

d) PAPEL​

Answer 1

Conte as vees que cada letra aparece:

CALADA

C: 1

A: 3

L: 1

D: 1

Total: 6

Divida o fatorial do total pela multiplicacao dos fatoriais:

$\dfrac{6!}{1!3!1!1!}=\dfrac{6!}{3!}=6\cdot5\cdot4=120$

Answer 2

$\mathtt{a)}~\mathsf{\underbrace{CALADA} _{P_6^3}=\dfrac{6!}{3!}}\\\mathsf{\dfrac{6\cdot5\cdot4\cdot \diagup\!\!\!\!3!}{\diagup\!\!\!\!3!}=120}\\\mathtt{b)}~\mathsf{\underbrace{BOLO}_{P_4^2}=\dfrac{4!}{2!}}\\\mathsf{\dfrac{4\cdot3\cdot \diagup\!\!\!\!2!}{\diagup\!\!\!\!2!}=12}\\\mathtt{c)}~\mathsf{\underbrace{VIVI}_{P_4^{2,2}}=\dfrac{4!}{2!\cdot2!}}\\\mathsf{\dfrac{\diagup\!\!\!\!4\cdot3\cdot\diagup\!\!\!\!2!}{\diagup\!\!\!\!2!\cdot \diagup\!\!\!\!2}=6}\\\mathtt{d)}~\mathsf{\underbrace{PAPEL}_{P_4^2}=\dfrac{4!}{2!}}\\\mathsf{\dfrac{4\cdot3\cdot \diagup\!\!\!\!2!}{\diagup\!\!\!\!2!}=12}$