Resolva os exercícios abaixo:
a) A11,3/C11,3 + 25 p5
b) A11,3 + C11,3
c) A2003,4/C2003,4 + 1
d) 20! + 19!/18!
e) 18! 27!/26! 16!
Soluções para a tarefa
An,x =n!/(n-x)!
Cn,x=n!/(n-x)!x!
a)
A11,3/C11,3 + 25 P5
[11!/(11-3)! ] / [11!/(11-3)!*3! + 25 * 5!
[11!/(11-3)! ] * [(11-3)!*3!/ 11! + 25 * 5!
[1/(11-3)! ] * [(11-3)!*3!/ 1 + 25 * 5!
[1/1 ] * [1*3!/ 1 + 25 * 5!
=3! +25*5!
=3*2*1 +25 * 5*4*3*2*1
= 6 + 3000
=3006
b)
A11,3 + C11,3
=11!/(11-3)! +11!/(11-3)!3!
=11!/8! +11!/8!3!
=11*10*9*8!/8! +11*10*9*8!/8!3!
=11*10*9 +11*10*9/3!
=11*10*9 +11*10*9/(3*2*1)
=11*10*9 +11*5*3
= 1155
c)
A2003,4/C2003,4 + 1
(2003!/(2003-4)!) / (2003!/(2003-4)!*4!) +1
(2003!/1999!) / (2003!/1999!*4!) +1
(2003!/1999!) * (1999!*4!)/ 2003! +1
(1/1999!) * (1999!*4!) +1
(1/1) * (1*4!) +1
4!+1
4*3*2*1 +1
=24+1
= 25
d)
# esta eu acho que tem parêntesis (20! + 19!)/18! .
(20! + 19!)/18!
(20*19*18! + 19*18!)/18!
=20*19 +19 = 399
e) 18! 27!/26! 16!
(18*17*16! 27*26!)/(26! 16!)
18*17*27
= 8262