Question

Simplifique a expressão:

a) 10! / 4! 6!    b) 9! / 2! 7!  c) 11! / 3! 8!   d) 3x6! / 4!

Answer 1

Hola.

a) 10! / 4! 6! = (10*9*8*7*6!)/4!6! =  10*9*8*7*/4*3*2*1 = 210
b) 9! / 2! 7!  = (9*8*7!)/2!7! = 9*8/2 = 36
c) 11! / 3! 8!  = (11*10*9*8!)/3!8! = 11*10*9/6 = 165
d) 3x6! / 4! = 3x(6*5*4!)/4! = 3x6*5 = 3*30 = 90

O que está em negrito é para simplificar. Certo?

Answer 2

$a)\;\dfrac{10!}{4!\times6!}=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times6!}=\dfrac{10\times9\times8\times7}{4\times3\times2}=10\times3\times7=210\\\\\\ b)\;\dfrac{9!}{2!\times7!}=\dfrac{9\times8\times7!}{2\times1\times7!}=\dfrac{9\times8}{2}=9\times4=36\\\\\\ c)\;\dfrac{11!}{3!\times8!}=\dfrac{11\times10\times9\times8!}{3\times2\times1\times8!}=\dfrac{11\times10\times9}{3\times2}=11\times5\times3=165\\\\\\ d)\;\dfrac{3\times6!}{4!}=\dfrac{3\times6\times5\times4!}{4!}=3\times6\times5=90$