Question

Calcule o numero de anagramas da palavra

a) batata
b)arara
c)tora
d)maria.

Com calculos e correto !!

Answer 1

Ops havia esquecido quando há palavras repetidas se resolve assim:
batata  6!/3!.2! =720/12 =60 possibilidades
arara 5!/3!*2=120/12=10 possibilidades
tora 4*3*2*1=24 possibilidades
maria 5!/2!=120/2=60 possibilidades

Answer 2

$\tt{a)}~\sf{\underbrace{BATATA}_{P_6^{3,2}}=\dfrac{6!}{3!\cdot2!}}\\\mathsf{\dfrac{ \diagup\!\!\!\! 6\cdot5\cdot4\cdot\diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot \diagup\!\!\!\!2}=3\cdot5\cdot4=60}\\\tt{b)}~\sf{\underbrace{ARARA}_{P_5^{3,2}}=\dfrac{5!}{3!\cdot2!}}\\\sf{\dfrac{5\cdot \diagup\!\!\!\!4\cdot \diagup\!\!\!\!3!}{\diagup\!\!\!\!3!\cdot \diagup\!\!\!\!2}=5\cdot2=10}\\\tt{c)}~\sf{\underbrace{TORA}_{P_4}=4!=24}\\\tt{d)}~\sf{\underbrace{MARIA}_{P_5^2}=\dfrac{5!}{2!}}\\\sf{\dfrac{5\cdot4\cdot3\cdot \diagup\!\!\!\!2!}{\diagup\!\!\!\!2!}=60}$