Binomialkoeffizenten
Author: R. Ordowski

N

T

T

N

N

T

T

N

T

N

T

N

T

N

T

N

T

N

N

T

N

T

N

T

N

T

N

T

N

p

q

p

q

p

q

p^2

pq

pq

q^2

p

q

p

q

p

q

p^3

p^2 q

p^2 q

p q^2

p^2 q

p q^2

p q^2

q^3

Ord 2009

Anzahl der Pfade:

Trefferzahl:

Bernoullikette der Länge

p

q

p

q

p

q

p

q

p

q

p

q

p

q

p

q

p^4

p^3 q

p^3 q

p^2 q^2

p^3 q

p^2 q^2

p^2 q^2

pq^3

p^3 q

p^2 q^2

p^2 q^2

pq^3

p^2 q^2

pq^3

pq^3

q^4

0 < p < 1
q = 1 - p

Ord 2009

kk4 = 0 (slider from 0 to 4, step 1)
kk2 = 0 (slider from 0 to 2, step 1)
n = 4 (slider from 1 to 4, step 1)
kk1 = 0 (slider from 0 to 1, step 1)
kk3 = 0 (slider from 0 to 3, step 1)
A = (6.991382222206089, 5.897321258450444)
B: (x(A) + n + 1.0, 3.0)
C: (x(A) - n - 1.0, 3.0)
D: (x(C) - n, 0.0)
E: (x(C) + n / 2.0, 0.0)
F: (x(B) + n, 0.0)
G: (x(B) - n / 2.0, 0.0)
H: (x(D) - n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
I: (x(D) + n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
J: (x(E) - n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
K: (x(E) + n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
L: (x(G) - n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
M: (x(G) + n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
N: (x(F) - n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
O: (x(F) + n / 3.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 3.0)
P: (x(H) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
Q: (x(H) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
R: (x(I) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
S: (x(I) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
T: (x(J) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
U: (x(J) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
V: (x(K) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
W: (x(K) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
Z: (x(L) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
A_1: (x(L) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
B_1: (x(M) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
C_1: (x(M) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
D_1: (x(N) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
E_1: (x(N) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
F_1: (x(O) - n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
G_1: (x(O) + n / 6.0, -1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 6.0)
a = Segment(A, C)
b = Segment(A, B)
c = Segment(C, D)
d = Segment(C, E)
e = Segment(B, G)
f = Segment(B, F)
k = If(n ≟ 1.0, kk1, If[n ≟ 2.0, kk2, If[n ≟ 3.0, kk3, If[n ≟ 4.0, kk4]]])
g = Segment(A, C)
h = Segment(C, D)
i = Segment(A, B)
j = Segment(B, F)
l = Segment(C, E)
m = Segment(B, G)
p = Segment(D, H)
q = Segment(D, I)
r = Segment(E, J)
s = Segment(E, K)
t = Segment(G, L)
a_1 = Segment(G, M)
b_1 = Segment(F, N)
c_1 = Segment(F, O)
d_1 = Segment(A, B)
e_1 = Segment(B, F)
f_1 = Segment(F, O)
g_1 = Segment(A, C)
h_1 = Segment(C, D)
i_1 = Segment(D, H)
j_1 = Segment(D, I)
k_1 = Segment(C, E)
l_1 = Segment(B, G)
m_1 = Segment(E, J)
n_1 = Segment(E, K)
p_1 = Segment(G, L)
q_1 = Segment(G, M)
r_1 = Segment(F, N)
s_1 = Segment(F, O)
o = Binomial(n, k)
u = Binomial(n, k)
Text14: "\left(\begin{array}" + n + " \\" + k + " \\ \end{array}\right) =" + u
t_1 = Segment(H, P)
a_2 = Segment(H, Q)
b_2 = Segment(I, R)
c_2 = Segment(I, S)
d_2 = Segment(J, T)
e_2 = Segment(J, U)
f_2 = Segment(K, V)
g_2 = Segment(K, W)
h_2 = Segment(L, Z)
i_2 = Segment(L, A_1)
j_2 = Segment(M, B_1)
k_2 = Segment(M, C_1)
l_2 = Segment(N, D_1)
m_2 = Segment(N, E_1)
n_2 = Segment(O, F_1)
p_2 = Segment(O, G_1)
q_2 = Segment(A, C)
r_2 = Segment(A, B)
s_2 = Segment(C, D)
t_2 = Segment(C, E)
a_3 = Segment(B, G)
b_3 = Segment(B, F)
c_3 = Segment(D, H)
d_3 = Segment(D, I)
e_3 = Segment(E, J)
f_3 = Segment(E, K)
g_3 = Segment(G, L)
h_3 = Segment(G, M)
i_3 = Segment(F, N)
j_3 = Segment(F, O)
k_3 = Segment(H, P)
l_3 = Segment(H, Q)
m_3 = Segment(I, R)
n_3 = Segment(I, S)
p_3 = Segment(J, T)
q_3 = Segment(J, U)
r_3 = Segment(K, V)
s_3 = Segment(K, W)
t_3 = Segment(L, Z)
a_4 = Segment(L, A_1)
b_4 = Segment(M, B_1)
c_4 = Segment(N, D_1)
d_4 = Segment(N, E_1)
e_4 = Segment(O, F_1)
f_4 = Segment(O, G_1)
g_4 = Segment(M, C_1)
h_4 = Segment(A, B)
i_4 = Segment(A, C)
Text36: "k = " + k