matematicarlos analise combinatoria - exercicios de aprendizagem

7/29/2019 Matematicarlos Analise Combinatoria - Exercicios de Aprendizagem

1/17

CARLOS EDUARDO MORAES PIRES

www.matematicarlos.com.br1

6. EDIO 2013


2/17



Desvende os segredos do clculo mental com a revista Matemtica de Todos n 1.

Pea j a sua em www.matematicadetodos.com.br


3/17



INTRODUO

1. Didatia!"#t"$ di%ida a A#&'i(" C)!*i#at+,ia "! 3 -,/)(.

2. E(,"%a a di","#a *&(ia "#t," a /",!ta)$ a,,a#) " )!*i#a).

4ATORIA5

3. D"i#a at),ia'.

. Ca''" )( at),iai( a*ai7)8

a9 :;

*9 ;

9 3;

d9 2;

"9 1;

9 0;


4/17



:. E(,"%a )!) (" '!",) #a a''ad),a i"#t?ia@

. O =" a#a-,a!a@

. Qai( () )( a#a-,a!a( da /a'a%,a VIA@

. Qa#t)( a#a-,a!a( t"! a /a'a%,a8

a9 TIO

*9 5EO

9 CE5A

d9 O5A

"9 VASCO

9 ENFO

-9 CAR5OS

G9 CAE5O

PERMUTA O


5/17


www.matematicarlos.com.br

10. C)! 1$2 " 3$ =a#t)( #>!",)( d" 3 a'-a,i(!)( /)d"!)( ),!a, ("! ,"/"tiH')(@

11. C)! 1$ 2 " 3$ =a#t)( #>!",)( d" 3 a'-a,i(!)( /)d"!)( ),!a,$ /)d"#d),"/"tiH')(@

12. Qa#ta( /)((i*i'idad"( /)d"!)( ),!a, ! #>!",) d" a'-a,i(!)( di(ti#t)()! 3$$: " 6@

13. E (" /d",!)( ,"/"ti, )( a'-a,i(!)($ =a#ta( /)((i*i'idad"( t","!)(@

1. S"a! )( a'-a,i(!)( 1$2$3$ " :. Q","#d) ),!a, ! #>!",) )! : a'-a,i(!)($=a#ta( /)((i*i'idad"( "7i(t"!$ (" #) /d", ,"/"ti, )( a'-a,i(!)(@

1:. E (" /d", ,"/"ti,@


6/17


www.matematicarlos.com.br!

16. U! /,)"((), /a,ti'a, t"! a'#)(. T)da( a( a'a( "'" !da )( a'#)( d"'-a,$ /a,a ="$ a="'" =" "(ta%a ')#-" d"'"$ /)((a ia, /",t). D"/)i( d" =a#t)(dia( "'" i,& ,"/"ti, ",ta /)(i)@

1. U!a a!?'ia d" : /"(()a( /)d"! ("#ta,H(" !"(a /a,a a'!)a, "! =a#ta(/)(iJ"( di","#t"(@

1. Qa#t)( #>!",)( /a,"( d" 3 a'-a,i(!)( /)d"!)( ),!a, )! 1$2 " 3 /)d"#d),"/"ti, )( a'-a,i(!)(@

1. E (" ),"! )! a'-a,i(!)( di(ti#t)(@

PERMUTA O COM RESTRI O


7/17


www.matematicarlos.com.br"

20. Qa#t)( #>!",)( ?!/a,"( /)d"!)( ),!a, )! )( #>!",)( 1$2 " 3$ /)d"#d),"/"ti, )( a'-a,i(!)(@

21. E (" ),"! di(ti#t)(@

22. C)! )( a'-a,i(!)( 1$2$3 " $ /)d"!)( ),!a, =a#t)( #>!",)( d" a'-a,i(!)(=" t",!i#"! )! 3$ /)d"#d) ,"/"ti, )( a'-a,i(!)(@

23. E (" ),"! di(ti#t)(@

2. P)d"#d) ,"/"ti, )( a'-a,i(!)($ =a#t)( #>!",)( d" : a'-a,i(!)( /)d"!)(),!a, )! 1$2$3$ " : =" )!""! )! 2 " t",!i#"! )! :@


8/17


www.matematicarlos.com.br#

2:. E (" ),"! di(ti#t)(@

26. C)! )( a'-a,i(!)( 0$1$2$3$ " :$ /)d"!)( ),!a, =a#t)( #>!",)( d" 6a'-a,i(!)($ /)d"#d) ,"/"tiH')(@

2. E (" ),"! di(ti#t)(@

2. Qa#t)( a#a-,a!a( () /)((?%"i( aK", )! a /a'a%,a CEU t",!i#a#d) )! E@

2. Qa#t)( a#a-,a!a( /)d"! (", "it)( )! a /a'a%,a CEU #) /)d"#d) t",!i#a,)! a '"t,a E@


9/17


www.matematicarlos.com.br$

30. Qa#t)( a#a-,a!a( /)d"! (", ),!ad)( )! a /a'a%,a BRANCO ("! t",!i#a,)! a '"t,a B@

31. Qa#t)( a#a-,a!a( /)d"!)( ),!a, )! a /a'a%,a BO5A t"#d) a( '"t,a( BO("!/," #ta(@

32. C)! a /a'a%,a 5EITO /)d"!)( ),!a, =a#t)( a#a-,a!a( )! a( '"t,a( 5T("!/," #ta(@

33. Qa#t)( a#a-,a!a( /)d"!)( ),!a, )! a /a'a%,a BO5A t"#d) a( '"t,a( BO("!/," #ta( " #"(ta ),d"!@

3. C)! a /a'a%,a 5EITO /)d"!)( ),!a, =a#t)( a#a-,a!a( )! a( '"t,a( 5T("!/," #ta( " #"(ta ),d"!@


10/17


www.matematicarlos.com.br1%

3:. Qa#t)( #>!",)( d" 2 a'-a,i(!)( di(ti#t)( /)d"!)( ),!a, )! 1$2 " 3@

36. C)! 1$2$3 " $ =a#t)( #>!",)( d" 3 a'-a,i(!)( di(ti#t)( /)d"!)( ),!a, @

3. Qa#t)( #>!",)( d" 2 a'-a,i(!)( di(ti#t)( /)d"H(" ),!a, )! 1$2$3 " @

3. Qa#t)( #>!",)( d" 2 a'-a,i(!)( di(ti#t)( /)d"!)( ),!a, )! 1$2$3$$:$6 "@

3. A( /'aa( d" a,,) () ),!ada( /), 3 '"t,a( " #>!",)(. Qa#ta( /'aa(di","#t"( /)d"! (", a*,iada($ /)d"#d) ,"/"ti, )( a'-a,i(!)( " '"t,a(@

ARRANJO


11/17



0. O( #>!",)( d" t"'")#" #) E(/?,it) Sa#t) () ),!ad)( /), a'-a,i(!)(.Qa#t)( #>!",)( /)d"! (", ),!ad)( )#(id",a#d) =" )( a'-a,i(!)( /)d"! (",,"/"tid)( "! =a'=", /)(i)@

1. Qa#t)( #>!",)( d" .000 .000 /)d"!)( ),!a, )! )( a'-a,i(!)( 3$$:$6 " ("! ,"/"tiH')(@

2. Qa#t)( #>!",)( d" 2.000 a .000 /)d"!)( ),!a, )! )( a'-a,i(!)( 1$2$3 " ("! ,"/"tiH')(@

3. A) 'a#a, 2 dad)($ =a#t)( ,"('tad)( di","#t"( /)d"! ai,@

. E a) 'a#a, 2 !)"da(@

:. U!a ("#Ga d" "H!ai' )i ),!ada /), 6 a'-a,i(!)(. O (&,i) "(=""H(" d"'a" /,"i(a ,"(-at&H'a. C)!) "'" #) t"! /ai


12/17



6. E (" ),"! a'-a,i(!)( di(ti#t)(@

. Pa,a ("-,a#a d)( (&,i)( d" *a#)$ a'! da ("#Ga )! #>!",)($"(ta*"'""H(" +di-)( )! 3 '"t,a(. Qa#ta( ("#Ga( di","#t"( /)d"H(" ),!a,)! "((a( t,


13/17



:1. Qa#t)( #>!",)( d" a'-a,i(!)( /)d"H(" aK", )! 0$1$2$3$ " :@

:2. U(a#d) #!",ai( d" 1 a $ =a#t)( #>!",)( /a,"( d" 3 a'-a,i(!)( /)d"! (",),!ad)( @

:3. Sa*"#d) =" a )!/a#Gia d" t"'")#ia t"! )( #>!",)( d" ("( "''a,"()!"a#d) /), " $ =a#t)( #>!",)( di","#t"( "'a /)d" -",a,@

:.Qai( () )( a#a-,a!a( ),!ad)( )! a /a'a%,a A5A@

ARRANJO COM RESTRI O

PERMUTA O E ARRANJO COM REPETI O


14/17



::. E da /a'a%,a BA5A@

:6. Qa' ) !t)d) /,&ti) /a,a a''a, /",!ta) )! ,"/"ti)@

:. Ca''" a =a#tidad" d" a#a-,a!a( /)((?%"i( da /a'a%,a ACACA.

:. C)! 1$ 1$ 2$ 3$ $ $ " :$ =a#t)( #>!",)( d" 3 a'-a,i(!)( /)d"! (",),!ad)(@

:. Qa' ) !t)d) /,&ti) /a,a a''a, )!*i#a)@

&'('

')

*n*

n+ *n

=

COMBINA O


15/17



60. Ca''"8

a9 C6$2 *9 C1$10

9 C$6 d9

3

4 "9

4

+

61. Ca,')($ Eda,d)$ ),a"( " Pi,"( %) di(/ta, ! t),#"i) d" 7ad,"K. Sa*"#d)=" "'"( )-a! a/"#a( !a %"K )! ada ad%",(&,i) " ) %"#"d), (",& a="'" =")*ti%", ) !ai), #>!",) d" /)#t)($ =a#t)( )-)( (",) ,"a'iKad)(@

62. A) "()'G", ! (),%"t" d" 2 *)'a($ /)d"H(" )/ta, /"')( ("-i#t"( (a*),"(8!),a#-)$ G))'at"$ )) " aa. Qa#ta( )/J"( ) 'i"#t" t"!@


16/17


www.matematicarlos.com.br1!

n

n'

63. D" =a#t)( !)d)( /)d"!)( ),!a, !a ,)da )! : ,ia#a(@

6. Qa#ta( ,)da( d" i,a#da /)d"!)( ),!a, )! 6 ,ia#a(@

6:. S"$ #!a ,"#i) d" /,"(id"#t"( a( ,"#iJ"( a)#t""(("! a) ,"d), d" !a!"(a$ d" =a#ta( !a#"i,a( "'"( /)d",ia! (", ),-a#iKada(@

66. Na ,"#i) itada ai!a$ (" d)i( /,"(id"#t"( #) /d"(("! ("#ta, #t)($=a#ta( ),!aJ"( /)d",ia! (", "ita(@

PERMUTA O CIRCULAR


17/17

matematicarlos analise combinatoria - exercicios de aprendizagem

Documents