3つのさいころの場合の数

大中小の３つのさいころを投げるとき、目の数の和が６になる組み合わせを樹形図で数えてみよう。

大中小の３個のさいころを投げるとき、
目の和が６になるのは何通りあるか。

大

中

小

1

2

3

4

1

2

3

4

1

2

3

1

2

1

4

3

2

1

3

2

1

2

1

1

10通り

スライダを
動かしてみよう。

A = (0.74, 2)
a: x = x(A)
B = Point(a)
C = Point(a)
D = Point(a)
E = (3.42, 3.18)
b: x = x(E)
F: (x(E), y(E) - 0.8)
G: (x(E), y(E) - 1.6)
H: (x(E), y(E) - 2.4)
I: (x(E), y(E) - 3.2)
J: (x(E), y(E) - 4)
K: (x(E), y(E) - 4.8)
L: (x(E), y(E) - 5.6)
M: (x(E), y(E) - 6.4)
N: (x(E), y(E) - 7.2)
E_1 = (6.56, 3.16)
b_1: x = x(E_1)
F_1: (x(E_1), y(E_1) - 0.8)
G_1: (x(E_1), y(E_1) - 1.6)
H_1: (x(E_1), y(E_1) - 2.4)
I_1: (x(E_1), y(E_1) - 3.2)
J_1: (x(E_1), y(E_1) - 4)
K_1: (x(E_1), y(E_1) - 4.8)
L_1: (x(E_1), y(E_1) - 5.6)
M_1: (x(E_1), y(E_1) - 6.4)
N_1: (x(E_1), y(E_1) - 7.2)
O = (3, 3.24)
P = (1.38, 2.2)
c = Segment(O, P)
Q = (3.04, 2.56)
d = Segment(P, Q)
R = (3.08, 1.78)
e = Segment(P, R)
S = (3, 1)
f = Segment(P, S)
T = (1.32, -0.64)
U = (3.02, 0.14)
g = Segment(T, U)
V = (3.02, -0.66)
h = Segment(T, V)
W = (3.08, -1.42)
i = Segment(T, W)
Z = (1.36, -2.76)
A_1 = (3.06, -2.22)
j = Segment(Z, A_1)
B_1 = (3, -3)
k = Segment(Z, B_1)
C_1 = (1.36, -3.84)
D_1 = (2.98, -3.84)
l = Segment(C_1, D_1)
O_1 = (4.02, 3.3)
P_1 = (6.12, 3.32)
m = Segment(O_1, P_1)
O_2 = (4, 2.48)
P_2 = (6.1, 2.5)
m_1 = Segment(O_2, P_2)
O_3 = (4, 1.76)
P_3 = (6.1, 1.78)
m_2 = Segment(O_3, P_3)
O_4 = (4, 1)
P_4 = (6.1, 1.02)
m_3 = Segment(O_4, P_4)
O_5 = (4.02, 0.14)
P_5 = (6.12, 0.16)
m_4 = Segment(O_5, P_5)
O_6 = (4, -0.7)
P_6 = (6.1, -0.68)
m_5 = Segment(O_6, P_6)
O_7 = (4.02, -1.48)
P_7 = (6.12, -1.46)
m_6 = Segment(O_7, P_7)
O_8 = (4.02, -2.24)
P_8 = (6.12, -2.22)
m_7 = Segment(O_8, P_8)
O_9 = (4, -3)
P_9 = (6.1, -2.98)
m_8 = Segment(O_9, P_9)
O_{10} = (4, -3.8)
P_{10} = (6.1, -3.78)
m_9 = Segment(O_{10}, P_{10})
n = 1 (slider from 1 to 3, step 1)