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COMBINATORIA Patricia Casal París
VARIACIONES SIN REPETICIÓN
V{a, b, c}, 2             { {a,b} , {b,a} , {a,c} , {c,a} , {b,c} , {c,b} }
V3, 2           6
V{a, b, c, d}, 2              { {a,b} , {b,a} , {a,c} , {c,a} , {a,d} , {d,a} , {b,c} , {c,b} , {b,d} , {d,b} , {c,d} , {d,c} }
variaciones( {a,b,c,d},2)                        { {a,b} , {b,a} , {a,c} , {c,a} , {a,d} , {d,a} , {b,c} , {c,b} , {b,d} , {d,b} , {c,d} , {d,c} }
V4, 2    12
V{a, b, c, d}, 3
       { {a,b,c} , {a,c,b} , {b,a,c} , {b,c,a} , {c,a,b} , {c,b,a} , {a,b,d} , {a,d,b} , {b,a,d} , {b,d,a} , {d,a,b} , {d,b,a} , {a,c,d} , {a,d,c} , {c,a,d} , {c,d,a} , {d,a,c} , {d,c,a} , {b,c,
V4, 3         24


COMBINACIONES SIN REPETICIÓN
C{a, b, c}, 2             { {a,b} , {a,c} , {b,c} }
C3, 2            3
C{a, b, c, d}, 2              { {a,b} , {a,c} , {a,d} , {b,c} , {b,d} , {c,d} }
C4, 2            6
C{a, b, c, d}, 3              { {a,b,c} , {a,b,d} , {a,c,d} , {b,c,d} }
combinaciones ( {a,b,c,d},2)                            { {a,b} , {a,c} , {a,d} , {b,c} , {b,d} , {c,d} }
C4, 3   4


PERMUTACIONES SIN REPETICIÓN DE n ELEMENTOS
P{a, b, c}               { {a,b,c} , {a,c,b} , {b,a,c} , {b,c,a} , {c,a,b} , {c,b,a} }
permutaciones( 3)                      6
P3    6
P{a, b, c, d}
       { {a,b,c,d} , {a,b,d,c} , {a,c,b,d} , {a,c,d,b} , {a,d,b,c} , {a,d,c,b} , {b,a,c,d} , {b,a,d,c} , {b,c,a,d} , {b,c,d,a} , {b,d,a,c} , {b,d,c,a} , {c,a,b,d} , {c,a,d,b} , {c,b,a,d}
P4         24


VARIACIONES CON REPETICIÓN
VR{a, b, c}, 2                { {a,a} , {a,b} , {a,c} , {b,a} , {b,b} , {b,c} , {c,a} , {c,b} , {c,c} }
VR3, 2               9
VR{a, b, c, d}, 2               { {a,a} , {a,b} , {a,c} , {a,d} , {b,a} , {b,b} , {b,c} , {b,d} , {c,a} , {c,b} , {c,c} , {c,d} , {d,a} , {d,b} , {d,c} , {d,d} }
variaciones_con_repetición( 4,2)                            16
VR4, 2    16
VR{a, b, c, d}, 3
      { {a,a,a} , {a,a,b} , {a,a,c} , {a,a,d} , {a,b,a} , {a,b,b} , {a,b,c} , {a,b,d} , {a,c,a} , {a,c,b} , {a,c,c} , {a,c,d} , {a,d,a} , {a,d,b} , {a,d,c} , {a,d,d} , {b,a,a} , {b,a,b} , {b,a,c}
VR4, 3         64

COMBINACIONES CON REPETICIÓN
CR {a, b, c}, 2               { {a,a} , {a,b} , {a,c} , {b,b} , {b,c} , {c,c} }
CR 3, 2              6
CR {a, b, c, d}, 2              { {a,a} , {a,b} , {a,c} , {a,d} , {b,b} , {b,c} , {b,d} , {c,c} , {c,d} , {d,d} }
CR 4, 2              10
combinaciones_con_repetición( 4,2)                 10
CR {a, b, c, d}, 3
      { {a,a,a} , {a,a,b} , {a,a,c} , {a,a,d} , {a,b,b} , {a,b,c} , {a,b,d} , {a,c,c} , {a,c,d} , {a,d,d} , {b,b,b} , {b,b,c} , {b,b,d} , {b,c,c} , {b,c,d} , {b,d,d} , {c,c,c} , {c,c,d} , {c,d,
CR 4, 3         20

PERMUTACIONES CON REPETICIÓN
  {a, a, b, b}
P4                           { {a,a,b,b} , {a,b,a,b} , {a,b,b,a} , {b,a,a,b} , {b,a,b,a} , {b,b,a,a} }
 2, 1, 1
P4                   12
permutaciones_con_repetición( 4,2,1,1)                                12
 {a, a, a, b}
P4                        { {a,a,a,b} , {a,a,b,a} , {a,b,a,a} , {b,a,a,a} }
 3, 1
P4            4

TRIÁNGULO DE TARTAGLIA

     _       _           _       _     0     _      _       _     _
                                       0
     _       _           _       1     _     1      _       _     _
                                 0           1                                   ____1____
                         2             2            2                            ___1_1___
     _       _                   _           _              _     _              __1_2_1__
                         0             1            2                            _1_3_1_1_
     _       3           _       3     _     3      _       3     _              1_4_6_4_1
             0                   1           0              3
     4       _           4       _     4     _      4       _     4
     0                   1             2            3             4


                                                                                                             1/8
d} , {b,d,c} , {c,b,d} , {c,d,b} , {d,b,c} , {d,c,b} }




} , {c,b,d,a} , {c,d,a,b} , {c,d,b,a} , {d,a,b,c} , {d,a,c,b} , {d,b,a,c} , {d,b,c,a} , {d,c,a,b} , {d,c,b,a} }




} , {b,a,d} , {b,b,a} , {b,b,b} , {b,b,c} , {b,b,d} , {b,c,a} , {b,c,b} , {b,c,c} , {b,c,d} , {b,d,a} , {b,d,b} , {b,d,c} , {b,d,d} , {c,a,a} , {c,a,b} , {c,a,c} , {c,a,d} , {c,b,a} , {c,b,b} , {




d} , {d,d,d} }




                                                                                               2/8
c,b,c} , {c,b,d} , {c,c,a} , {c,c,b} , {c,c,c} , {c,c,d} , {c,d,a} , {c,d,b} , {c,d,c} , {c,d,d} , {d,a,a} , {d,a,b} , {d,a,c} , {d,a,d} , {d,b,a} , {d,b,b} , {d,b,c} , {d,b,d} , {d,c,a} , {d,c,




                                                                                              3/8
b} , {d,c,c} , {d,c,d} , {d,d,a} , {d,d,b} , {d,d,c} , {d,d,d} }




                                                                   4/8
5/8
6/8
7/8
8/8

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Wiris

  • 1. COMBINATORIA Patricia Casal París VARIACIONES SIN REPETICIÓN V{a, b, c}, 2 { {a,b} , {b,a} , {a,c} , {c,a} , {b,c} , {c,b} } V3, 2 6 V{a, b, c, d}, 2 { {a,b} , {b,a} , {a,c} , {c,a} , {a,d} , {d,a} , {b,c} , {c,b} , {b,d} , {d,b} , {c,d} , {d,c} } variaciones( {a,b,c,d},2) { {a,b} , {b,a} , {a,c} , {c,a} , {a,d} , {d,a} , {b,c} , {c,b} , {b,d} , {d,b} , {c,d} , {d,c} } V4, 2 12 V{a, b, c, d}, 3 { {a,b,c} , {a,c,b} , {b,a,c} , {b,c,a} , {c,a,b} , {c,b,a} , {a,b,d} , {a,d,b} , {b,a,d} , {b,d,a} , {d,a,b} , {d,b,a} , {a,c,d} , {a,d,c} , {c,a,d} , {c,d,a} , {d,a,c} , {d,c,a} , {b,c, V4, 3 24 COMBINACIONES SIN REPETICIÓN C{a, b, c}, 2 { {a,b} , {a,c} , {b,c} } C3, 2 3 C{a, b, c, d}, 2 { {a,b} , {a,c} , {a,d} , {b,c} , {b,d} , {c,d} } C4, 2 6 C{a, b, c, d}, 3 { {a,b,c} , {a,b,d} , {a,c,d} , {b,c,d} } combinaciones ( {a,b,c,d},2) { {a,b} , {a,c} , {a,d} , {b,c} , {b,d} , {c,d} } C4, 3 4 PERMUTACIONES SIN REPETICIÓN DE n ELEMENTOS P{a, b, c} { {a,b,c} , {a,c,b} , {b,a,c} , {b,c,a} , {c,a,b} , {c,b,a} } permutaciones( 3) 6 P3 6 P{a, b, c, d} { {a,b,c,d} , {a,b,d,c} , {a,c,b,d} , {a,c,d,b} , {a,d,b,c} , {a,d,c,b} , {b,a,c,d} , {b,a,d,c} , {b,c,a,d} , {b,c,d,a} , {b,d,a,c} , {b,d,c,a} , {c,a,b,d} , {c,a,d,b} , {c,b,a,d} P4 24 VARIACIONES CON REPETICIÓN VR{a, b, c}, 2 { {a,a} , {a,b} , {a,c} , {b,a} , {b,b} , {b,c} , {c,a} , {c,b} , {c,c} } VR3, 2 9 VR{a, b, c, d}, 2 { {a,a} , {a,b} , {a,c} , {a,d} , {b,a} , {b,b} , {b,c} , {b,d} , {c,a} , {c,b} , {c,c} , {c,d} , {d,a} , {d,b} , {d,c} , {d,d} } variaciones_con_repetición( 4,2) 16 VR4, 2 16 VR{a, b, c, d}, 3 { {a,a,a} , {a,a,b} , {a,a,c} , {a,a,d} , {a,b,a} , {a,b,b} , {a,b,c} , {a,b,d} , {a,c,a} , {a,c,b} , {a,c,c} , {a,c,d} , {a,d,a} , {a,d,b} , {a,d,c} , {a,d,d} , {b,a,a} , {b,a,b} , {b,a,c} VR4, 3 64 COMBINACIONES CON REPETICIÓN CR {a, b, c}, 2 { {a,a} , {a,b} , {a,c} , {b,b} , {b,c} , {c,c} } CR 3, 2 6 CR {a, b, c, d}, 2 { {a,a} , {a,b} , {a,c} , {a,d} , {b,b} , {b,c} , {b,d} , {c,c} , {c,d} , {d,d} } CR 4, 2 10 combinaciones_con_repetición( 4,2) 10 CR {a, b, c, d}, 3 { {a,a,a} , {a,a,b} , {a,a,c} , {a,a,d} , {a,b,b} , {a,b,c} , {a,b,d} , {a,c,c} , {a,c,d} , {a,d,d} , {b,b,b} , {b,b,c} , {b,b,d} , {b,c,c} , {b,c,d} , {b,d,d} , {c,c,c} , {c,c,d} , {c,d, CR 4, 3 20 PERMUTACIONES CON REPETICIÓN {a, a, b, b} P4 { {a,a,b,b} , {a,b,a,b} , {a,b,b,a} , {b,a,a,b} , {b,a,b,a} , {b,b,a,a} } 2, 1, 1 P4 12 permutaciones_con_repetición( 4,2,1,1) 12 {a, a, a, b} P4 { {a,a,a,b} , {a,a,b,a} , {a,b,a,a} , {b,a,a,a} } 3, 1 P4 4 TRIÁNGULO DE TARTAGLIA _ _ _ _ 0 _ _ _ _ 0 _ _ _ 1 _ 1 _ _ _ 0 1 ____1____ 2 2 2 ___1_1___ _ _ _ _ _ _ __1_2_1__ 0 1 2 _1_3_1_1_ _ 3 _ 3 _ 3 _ 3 _ 1_4_6_4_1 0 1 0 3 4 _ 4 _ 4 _ 4 _ 4 0 1 2 3 4 1/8
  • 2. d} , {b,d,c} , {c,b,d} , {c,d,b} , {d,b,c} , {d,c,b} } } , {c,b,d,a} , {c,d,a,b} , {c,d,b,a} , {d,a,b,c} , {d,a,c,b} , {d,b,a,c} , {d,b,c,a} , {d,c,a,b} , {d,c,b,a} } } , {b,a,d} , {b,b,a} , {b,b,b} , {b,b,c} , {b,b,d} , {b,c,a} , {b,c,b} , {b,c,c} , {b,c,d} , {b,d,a} , {b,d,b} , {b,d,c} , {b,d,d} , {c,a,a} , {c,a,b} , {c,a,c} , {c,a,d} , {c,b,a} , {c,b,b} , { d} , {d,d,d} } 2/8
  • 3. c,b,c} , {c,b,d} , {c,c,a} , {c,c,b} , {c,c,c} , {c,c,d} , {c,d,a} , {c,d,b} , {c,d,c} , {c,d,d} , {d,a,a} , {d,a,b} , {d,a,c} , {d,a,d} , {d,b,a} , {d,b,b} , {d,b,c} , {d,b,d} , {d,c,a} , {d,c, 3/8
  • 4. b} , {d,c,c} , {d,c,d} , {d,d,a} , {d,d,b} , {d,d,c} , {d,d,d} } 4/8
  • 5. 5/8
  • 6. 6/8
  • 7. 7/8
  • 8. 8/8