Pascal's Triangle
Date: 13 November 2014

Use Pascal's triangle to calculate combinations.  The "n" represents the row number and the "m" represents the number within that row. Use the sliders to figure out different combinations. 

For example, say we wanted to find "4 choose 2." We would slide the sliders to n=4 and m=2.  This would give us the answer for how many times we can choose 2 things from a set of 4. 

To reset the sliders, simply press the "Set n, m = 0" button.

Ver filas

Múltiplos de

Horizontales

Oblicuas

O = (1.92, 5)
U: O + (1, 0)
polígono1, g, h, i, V = Polygon(O, U, 3)
n = 2 (slider from 0 to m, step 1)
m = 14 (slider from 0 to 100, step 1)
w = (0.6, -0.35)
c = false
H = (2.1, 5.2)
v1 = Vector(V, O)
v2 = Vector(O, U)
divisor = 2 (slider from 2 to 7, step 1)
e = false
f = Cell(4, 3)
j = OrthogonalLine(O, g)
k = OrthogonalLine(V, h)
W = Intersect(j, k)
poli, l, p, r, t, a_1, poli_2, Z, A_1, B_1, C_1 = Polygon(V, W, 6)
v3 = Vector(V, U)
A = (2.2, 5.18)
B2 = NaN
tex_{0, 0} = Text(1)
tex_{1, 0} = Text(1)
tex_{1, 1} = Text(1)
tex_{2, 0} = Text(1)
tex_{2, 1} = Text(2)
tex_{2, 2} = Text(1)
tex_{3, 0} = Text(1)
tex_{3, 1} = Text(3)
tex_{3, 2} = Text(3)
tex_{3, 3} = Text(1)
tex_{4, 0} = Text(1)
tex_{4, 1} = Text(4)
tex_{4, 2} = Text(6)
tex_{4, 3} = Text(4)
tex_{4, 4} = Text(1)
tex_{5, 0} = Text(1)
tex_{5, 1} = Text(5)
tex_{5, 2} = Text(10)
tex_{5, 3} = Text(10)
tex_{5, 4} = Text(5)
tex_{5, 5} = Text(1)
tex_{6, 0} = Text(1)
tex_{6, 1} = Text(6)
tex_{6, 2} = Text(15)
tex_{6, 3} = Text(20)
tex_{6, 4} = Text(15)
tex_{6, 5} = Text(6)
tex_{6, 6} = Text(1)
tex_{7, 0} = Text(1)
tex_{7, 1} = Text(7)
tex_{7, 2} = Text(21)
tex_{7, 3} = Text(35)
tex_{7, 4} = Text(35)
tex_{7, 5} = Text(21)
tex_{7, 6} = Text(7)
tex_{7, 7} = Text(1)
tex_{8, 0} = Text(1)
tex_{8, 1} = Text(8)
tex_{8, 2} = Text(28)
tex_{8, 3} = Text(56)
tex_{8, 4} = Text(70)
tex_{8, 5} = Text(56)
tex_{8, 6} = Text(28)
tex_{8, 7} = Text(8)
tex_{8, 8} = Text(1)
tex_{9, 0} = Text(1)
tex_{9, 1} = Text(9)
tex_{9, 2} = Text(36)
tex_{9, 3} = Text(84)
tex_{9, 4} = Text(126)
tex_{9, 5} = Text(126)
tex_{9, 6} = Text(84)
tex_{9, 7} = Text(36)
tex_{9, 8} = Text(9)
tex_{9, 9} = Text(1)
tex_{10, 0} = Text(1)
tex_{10, 1} = Text(10)
tex_{10, 2} = Text(45)
tex_{10, 3} = Text(120)
tex_{10, 4} = Text(210)
tex_{10, 5} = Text(252)
tex_{10, 6} = Text(210)
tex_{10, 7} = Text(120)
tex_{10, 8} = Text(45)
tex_{10, 9} = Text(10)
tex_{10, 10} = Text(1)
poli' = Translate(poli, Vector[(m * v1) + (n * v2)])
fila = Sequence(Translate[poli, Vector[(m * v1) + (k * v2)]], k, 0, m)
texto1: "\binom{" + (LaTeX[m]) + "}{" + (LaTeX[n]) + "} = \frac{" + (LaTeX[m]) + "!}{" + (LaTeX[m - n]) + "!·" + (LaTeX[n]) + "!}=" + (LaTeX[Binomial[m, n]]) + ""
multi3 = Join({Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 2, 2], i, 3, 4], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 5, 2], i, 6, 7], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 2, 5], i, 6, 7], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 8, 8], i, 9, 11]})
multi4 = Join({{Translate[poli, Vector[(4 * v1) + v2]]}, {Translate[poli, Vector[(4 * v1) + (3 * v2)]]}, {Translate[poli, Vector[(6 * v1) + (3 * v2)]]}, {Translate[poli, Vector[(10 * v1) + (5 * v2)]]}, Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 7, 3], i, 8, 10], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 3, 7], i, 8, 10]})
multi6 = Join({Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 7, 7], i, 9, 11], {Translate[poli, Vector[(4 * v1) + (2 * v2)]]}, {Translate[poli, Vector[(6 * v1) + v2]]}, {Translate[poli, Vector[(6 * v1) + (5 * v2)]]}})
multi7 = Join(Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 6, 6], i, 7, 11])
red = Sequence(Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, 0, i], i, 0, 13)
diago = Sequence(Translate[poli, Vector[(k * v1) + (n * v2)]], k, n, 13)
multi2 = Join({{Translate[poli, Vector[(2 * v1) + v2]]}, {Translate[poli, Vector[(10 * v1) + v2]]}, {Translate[poli, Vector[(10 * v1) + (9 * v2)]]}, {Translate[poli, Vector[(6 * v1) + v2]]}, {Translate[poli, Vector[(6 * v1) + (5 * v2)]]}, Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 3, 3], i, 4, 6], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 7, 7], i, 8, 11]})
a = false
b = true
multi5 = Join({Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 4, 4], i, 5, 8], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 9, 4], i, 10, 11], Sequence[Sequence[Translate[poli, Vector[(i * v1) + (j * v2)]], j, i - 4, 9], i, 10, 11]})