Question

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!

Answer 1

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