Question

1-determine o número de anagramas de cada palavra. a)Brasil b)banana c)vestibular d)Copacabana

Answer 1

a) Brasil = 720

b) Banana = 60

c) Vestibular = 3.628.800

d) Copacabana = 75.600

Answer 2

A) BRASIL

$p(n)=n!\\p(6)=6!\\p(6)=6*5*4*3*2*1\\p(6)=30*4*3*2*1\\p(6)=120*3*2*1\\p(6)=360*2*1\\p(6)=720*1\\p(6)=720$

B) BANANA

$6!=6*5*4*3*2=720\\=720/3!\\=720/3*2*1\\=720/6\\=120\\=120/2!\\=120/2*1\\=60$

C) VESTIBULAR

$6!=5*4*3*2*1=720\\5!= 5*4*3*2*1=120\\6!*5!=720*120=86.400$

D) COPACABANA

$P^{4,2}_{10} =10!/4!*2!\\P^{4,2}_{10} =10*9*8*7*6*5*4!/4!*2!\\P^{4,2}_{10} =151200/2\\P^{4,2}_{10} =75.600$