Question

Análise Combinatória, por favor? ):

Calcule $<var>\frac{P_ 5 + C_ 8_,_3 - A _6_,_3}{2P_3}</var>$

Calcule a expressão $<var>\frac{40!-39!}{41!}</var>$ 

Answer 1

$P_{n} =n!$
$C_{n,p} = \frac{n!}{p! (n-p)!}$

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

A) $P_{5} = 5! = 5.4.3.2.1$
$P_{5} = 120$

$C_{8,3} = \frac{8.7.6.5!}{3!(8-3)!} = 8.7= 56$

$A_{6,3} = \frac{6.5.4.3!}{(6-3)!} = 120$

$P_{3} = 3! = 6$

$\frac{P_{5} + C_{8,3} - A_{6,3} }{ 2P_{3} }$

$\frac{120 + 56 -120}{2.6}$

$\frac{56}{12} = \frac{14}{3}$

b) $\frac{40! - 39!}{41!} = \frac{40.39! - 39!}{41.40.39!} = \frac{40 -1}{41.40} = \frac{39}{1640}$