J

A

B

Ver lista

E

D

C

F

G

H

I

fe

+

+

-

-

K

L

M

N

O

Genera otras 10

variaciones

combinaciones

varicons

Variaciones sin repetición

Combinaciones

Variaciones con repetición

Combinaciones

Permutaciones

Ver el número de posibles diferentes

Se ha de partir de
elementos diferentes

Permutaciones con repetición

permutas

caso: 5
m = 8 (slider from 2 to 15, step 1)
A10: 10
n = 5 (slider from 1 to tope, step 1)
A1: 1
A2: 2
A3: (2 * A2) - A1
A4: (2 * A3) - A2
A5: (2 * A4) - A3
A6: (2 * A5) - A4
A7: (2 * A6) - A5
A8: (2 * A7) - A6
A9: (2 * A8) - A7
C1 = Textfield(B1)
C5 = Textfield(B5)
C4 = Textfield(B4)
C3 = Textfield(B3)
C2 = Textfield(B2)
C6 = Textfield(B6)
C7 = Textfield(B7)
C8 = Textfield(B8)
C9 = Textfield(B9)
C10 = Textfield(B10)
eles = First(B1:B15, m)
A11: (2 * A10) - A9
A12: (2 * A11) - A10
A13: (2 * A12) - A11
A14: (2 * A13) - A12
A15: (2 * A14) - A13
O = (0, 0)
C11 = Textfield(B11)
C12 = Textfield(B12)
C13 = Textfield(B13)
C14 = Textfield(B14)
C15 = Textfield(B15)
conrepes: caso ≟ 2
D1 = Sample(eles, n, false)
E1 = Sum(D1)
D2 = Sample(eles, n, false)
E2 = Sum(D2)
D3 = Sample(eles, n, false)
E3 = Sum(D3)
D4 = Sample(eles, n, false)
E4 = Sum(D4)
D5 = Sample(eles, n, false)
E5 = Sum(D5)
D6 = Sample(eles, n, false)
E6 = Sum(D6)
D7 = Sample(eles, n, false)
E7 = Sum(D7)
D8 = Sample(eles, n, false)
E8 = Sum(D8)
D9 = Sample(eles, n, false)
E9 = Sum(D9)
D10 = Sample(eles, n, false)
E10 = Sum(D10)
variaciones10 = TableText({E1:E10}, "v")
F1 = Sort(D1)
F2 = Sort(D2)
F3 = Sort(D3)
F4 = Sort(D4)
F5 = Sort(D5)
F6 = Sort(D6)
F7 = Sort(D7)
F8 = Sort(D8)
F9 = Sort(D9)
F10 = Sort(D10)
H1 = Sample(eles, n, true)
I1 = Sum(H1)
H2 = Sample(eles, n, true)
I2 = Sum(H2)
H3 = Sample(eles, n, true)
I3 = Sum(H3)
H4 = Sample(eles, n, true)
I4 = Sum(H4)
H5 = Sample(eles, n, true)
I5 = Sum(H5)
H6 = Sample(eles, n, true)
I6 = Sum(H6)
H7 = Sample(eles, n, true)
I7 = Sum(H7)
H8 = Sample(eles, n, true)
I8 = Sum(H8)
H9 = Sample(eles, n, true)
I9 = Sum(H9)
H10 = Sample(eles, n, true)
I10 = Sum(H10)
a: caso ≟ 1
variconrepes10 = TableText({I1:I10}, "v")
b: caso ≟ 2
c: caso ≟ 1
d: caso ≟ 2
e: caso ≟ 2
f: caso ≟ 2
rojo: 0
verde: 0
azul: 0
combinaciones10 = TableText({G1:G10}, "v")
texto33 = If(caso ≠ 3, " tomados de " + n + " en " + n + "", "")
G1 = Sum(F1)
G2 = Sum(F2)
G3 = Sum(F3)
G4 = Sum(F4)
G5 = Sum(F5)
G6 = Sum(F6)
G7 = Sum(F7)
G8 = Sum(F8)
G9 = Sum(F9)
G10 = Sum(F10)
g = false
p = Min(n, m - n)
textoprod: m + If[p > 1, " · " + (m - 1), ""] + (If[p > 2, " · " + (m - 2), ""]) + (If[p > 3, " · " + (m - 3), ""]) + (If[p > 4, " · " + (m - 4), ""])
trozotexto = If(p > 1, "=\frac{ " + (LaTeX[textoprod]) + "}{ " + (LaTeX[p]) + " !}", "")
textoC: "C_{" + (LaTeX[m]) + "," + (LaTeX[n]) + "}= \binom{" + (LaTeX[m]) + " }{ " + (LaTeX[n]) + "}= \frac{" + (LaTeX[m]) + "!}{" + (LaTeX[m - n]) + "!·" + (LaTeX[n]) + "!}" + (LaTeX[trozotexto]) + "=" + (LaTeX[Binomial[m, n]]) + ""
textoVR: "VR_{" + (LaTeX[m]) + "," + (LaTeX[n]) + "}=" + (LaTeX[m]) + "^{" + (LaTeX[n]) + "}=" + (LaTeX[m^(n)]) + ""
listam = Sequence(m)
listafactores = Append(Sequence["·" + (Element[listam, k]), k, m - 1, m - n + 1, -1], "")
frecus = Frequency(eles)
repes: Max[frecus] > 1
indicesrepes = RemoveUndefined(Sequence[If[Element[frecus, k] > 1, Element[frecus, k]], k, 1, Length[frecus]])
superíndices: "" + (If[Length[indicesrepes] > 1, ", " + (Element[indicesrepes, 2]), ""]) + "" + (If[Length[indicesrepes] > 2, ", " + (Element[indicesrepes, 3]), ""]) + "" + (If[Length[indicesrepes] > 3, ", " + (Element[indicesrepes, 4]), ""]) + ""
factoriales: "" + (If[Length[indicesrepes] > 1, "· " + (Element[indicesrepes, 2]) + "!", ""]) + "" + (If[Length[indicesrepes] > 2, "· " + (Element[indicesrepes, 3]) + "!", ""]) + "" + (If[Length[indicesrepes] > 3, "· " + (Element[indicesrepes, 4]) + "!", ""]) + ""
textoV: "V_{" + (LaTeX[m]) + "," + (LaTeX[n]) + "}=" + (LaTeX[m]) + "" + (LaTeX[Sum[listafactores]]) + "=" + (LaTeX[nPr[m, n]]) + ""
nn: n
D13 = Sample(eles, n, false)
E13 = Sum(D13)
D14 = Sample(eles, n, false)
E14 = Sum(D14)
D15 = Sample(eles, n, false)
E15 = Sum(D15)
D16 = Sample(eles, n, false)
E16 = Sum(D16)
D17 = Sample(eles, n, false)
E17 = Sum(D17)
D18 = Sample(eles, n, false)
E18 = Sum(D18)
D19 = Sample(eles, n, false)
E19 = Sum(D19)
D20 = Sample(eles, n, false)
E20 = Sum(D20)
D21 = Sample(eles, n, false)
E21 = Sum(D21)
D22 = Sample(eles, n, false)
E22 = Sum(D22)
permutaciones10 = TableText({E13:E22}, "v")
lir = Length(indicesrepes)
listafactoriales = If(Max[frecus] ≟ 1, {1}, Sequence[Element[indicesrepes, k]!, k, 1, Length[indicesrepes]])
productofactoriales = Product(listafactoriales)
textoP: "P_{" + (LaTeX[n]) + "}=" + (LaTeX[n]) + "!=" + (LaTeX[n!]) + ""
tope = If(conrepes ∨ caso ≟ 3, 15, m)
texto3: "" + textocaso + " 
de " + m + " elementos" + texto33 + ""
texto3p: "Permutaciones de " + n + " elementos"
textoPR: "PR_{" + (LaTeX[n]) + "}^{" + (LaTeX[Element[indicesrepes, 1]]) + "" + (LaTeX[superíndices]) + "}=\frac{" + (LaTeX[n]) + "!}{" + (LaTeX[Element[indicesrepes, 1]]) + "!" + (LaTeX[factoriales]) + "}=" + (LaTeX[n! / productofactoriales]) + ""