Question

Calcular a análise combinatória:
a) 6!
b) 4.2!
c) 0!+4!
d) 5!-4!
e) 10! / 3!7!
f) 15!13! / 14!12!
g) 12!3! / 15!
h) 7! / 4!+3!
l) (3!-0!) / 3!2!

Answer 1

Desenvolvendo os fatoriais : 


a)  6! = 6.5.4.3.2.1 = 30.24 = 720 


b) 4.2! = 4.(2.1) = 4.2 = 8 


c) 0! + 4! = 1 + 4.3.2.1 = 1 + 24 = 25 


d) 5! - 4! = 5.4.3.2.1 - 4.3.2.1 = 120 - 24 = 96 


e) 10!/3!.7! = 10.9.8.7!/3.2.1.7! = 10.9.8/3.2 = 10.3.4 = 120 


f) 15!.13!/14!.12! = 15.14!.13.12!/14!.12! = 15 . 13 = 195 


g) 12!.3!/15! = 12!.3.2.1/15.14.13.12! = 6/15.14.13 = 6/2 730 = 1/455


h) 7!/4!+3! = 7.6.5.4.3.2.1/4.3.2.1+3.2.1 = 5 040/24+6 = 5 040/30 = 168


i) (3!-0!)/3!2! = (3.2.1-1)/3.2.1.2.1 = (6-1)/6.2 = 5/12                           ok

Answer 2

Resposta:

Desenvolvendo os fatoriais : 

a)  6! = 6.5.4.3.2.1 = 30.24 = 720 

b) 4.2! = 4.(2.1) = 4.2 = 8 

c) 0! + 4! = 1 + 4.3.2.1 = 1 + 24 = 25 

d) 5! - 4! = 5.4.3.2.1 - 4.3.2.1 = 120 - 24 = 96 

e) 10!/3!.7! = 10.9.8.7!/3.2.1.7! = 10.9.8/3.2 = 10.3.4 = 120 

f) 15!.13!/14!.12! = 15.14!.13.12!/14!.12! = 15 . 13 = 195 

g) 12!.3!/15! = 12!.3.2.1/15.14.13.12! = 6/15.14.13 = 6/2 730 = 1/455

h) 7!/4!+3! = 7.6.5.4.3.2.1/4.3.2.1+3.2.1 = 5 040/24+6 = 5 040/30 = 168

i) (3!-0!)/3!2! = (3.2.1-1)/3.2.1.2.1 = (6-1)/6.2 = 5/12