Question

Utilisando a regra para resolução com fatoriais , encontre o resultado de cada expressão a) 4!+6! /3!+5! B) 5!+4!-2!/6!-3! C) 7!-4!+3!/3!

Answer 1

a) $\frac{4!+6!}{3!+5!}= \frac{(4.3.2.1)+(6.5.4.3.2.1)}{(3.2.1)+(5.4.3.2.1)} = \frac{(24)+(720)}{(6)+(120)} = \frac{744}{126} = \frac{124}{21}$

b) $\frac{5!+4!-2!}{6!-3!} = \frac{(5.4.3.2.1)+(4.3.2.1)-(2.1)}{(6.5.4.3.2.1)-(3.2.1)} = \frac{(120)+(24)-(2)}{(720)-(6)} = \frac{142}{714} = \frac{71}{357}$

c)$\frac{7!-4!+3!}{3!} = \frac{(7.6.5.4.3.2.1)-(4.3.2.1)+(3.2.1)}{(3.2.1)} = \frac{(5040)-(24)+(6)}{6} =837$