Question

Calcule: (Arranjo simples)
A6,2
A2,2
A5,2
A9,3
A7,4

Answer 1

Fórmula Análise Combinatória (arranjo):

$A_n_,_p = \frac{n!}{(n-p)!}$

Resolvendo:

$A_6_,_2 = \frac{6!}{(6-2)!} = \frac{6!}{4!} = \frac{6*5*4!}{4!} = 30 \\ \\ A_2_,_2 = \frac{2!}{(2-2)!} = \frac{2!}{0!} = 1 \\ \\ A_5_,_2 = \frac{5!}{(5-2)!} = \frac{5!}{3!} = \frac{5*4*3!}{3!} = 20 \\ \\ A_9_,_3 = \frac{9!}{(9-3)!} = \frac{9!}{6!} = \frac{9*8*7*6!}{6!} = 504 \\ \\ A_7_,_4 = \frac{7!}{(7-4)!} = \frac{7!}{4!} = \frac{7*6*5*4!}{4!} = 210$