重複組合

投擲\;2\;個相同的骰子，\;有幾種不同的結果？

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C^{6+2-1}_2=H^6_2

A = (1.16, 6.14)
list1 = Sequence(A + (0, 2 - 2 * j), j, 1, 6)
list2 = Sequence(A + (2, 2 - 2 * j), j, 1, 6)
list3 = Sequence(A + (4.2, 2 - 2 * j), j, 1, 6)
list4 = Sequence(A + (6.2, 2 - 2 * j), j, 1, 6)
list5 = Sequence(A + (8.4, 2 - 2 * j), j, 1, 6)
list6 = Sequence(A + (10.4, 2 - 2 * j), j, 1, 6)
list7 = Sequence(A + (12.6, 2 - 2 * j), j, 1, 6)
list8 = Sequence(A + (14.6, 2 - 2 * j), j, 1, 6)
list9 = Sequence(A + (16.8, 2 - 2 * j), j, 1, 6)
list10 = Sequence(A + (18.8, 2 - 2 * j), j, 1, 6)
list11 = Sequence(A + (21, 2 - 2 * j), j, 1, 6)
list12 = Sequence(A + (23, 2 - 2 * j), j, 1, 6)
s = 0 (slider from 0 to 5, step 1)
Poly11, a, b, c, d = Polygon(Element[list1, 1], Element[list1, 1] + (4, 0), Element[list1, 1] + (4, 2), Element[list1, 1] + (0, 2))
Poly12, e, f, g, h = Polygon(Element[list3, 1], Element[list3, 1] + (4, 0), Element[list3, 1] + (4, 2), Element[list3, 1] + (0, 2))
Poly13, i, j, k, l = Polygon(Element[list5, 1], Element[list5, 1] + (4, 0), Element[list5, 1] + (4, 2), Element[list5, 1] + (0, 2))
Poly14, m, n, p, q = Polygon(Element[list7, 1], Element[list7, 1] + (4, 0), Element[list7, 1] + (4, 2), Element[list7, 1] + (0, 2))
Poly15, r, t, a_1, b_1 = Polygon(Element[list9, 1], Element[list9, 1] + (4, 0), Element[list9, 1] + (4, 2), Element[list9, 1] + (0, 2))
Poly16, c_1, d_1, e_1, f_1 = Polygon(Element[list11, 1], Element[list11, 1] + (4, 0), Element[list11, 1] + (4, 2), Element[list11, 1] + (0, 2))
Poly21, g_1, h_1, i_1, j_1 = Polygon(Element[list1, 2], Element[list1, 2] + (4, 0), Element[list1, 2] + (4, 2), Element[list1, 2] + (0, 2))
Poly22, k_1, l_1, m_1, n_1 = Polygon(Element[list3, 2], Element[list3, 2] + (4, 0), Element[list3, 2] + (4, 2), Element[list3, 2] + (0, 2))
Poly23, p_1, q_1, r_1, s_1 = Polygon(Element[list5, 2], Element[list5, 2] + (4, 0), Element[list5, 2] + (4, 2), Element[list5, 2] + (0, 2))
Poly24, t_1, a_2, b_2, c_2 = Polygon(Element[list7, 2], Element[list7, 2] + (4, 0), Element[list7, 2] + (4, 2), Element[list7, 2] + (0, 2))
Poly25, d_2, e_2, f_2, g_2 = Polygon(Element[list9, 2], Element[list9, 2] + (4, 0), Element[list9, 2] + (4, 2), Element[list9, 2] + (0, 2))
Poly26, h_2, i_2, j_2, k_2 = Polygon(Element[list11, 2], Element[list11, 2] + (4, 0), Element[list11, 2] + (4, 2), Element[list11, 2] + (0, 2))
Poly31, l_2, m_2, n_2, p_2 = Polygon(Element[list1, 3], Element[list1, 3] + (4, 0), Element[list1, 3] + (4, 2), Element[list1, 3] + (0, 2))
Poly32, q_2, r_2, s_2, t_2 = Polygon(Element[list3, 3], Element[list3, 3] + (4, 0), Element[list3, 3] + (4, 2), Element[list3, 3] + (0, 2))
Poly33, a_3, b_3, c_3, d_3 = Polygon(Element[list5, 3], Element[list5, 3] + (4, 0), Element[list5, 3] + (4, 2), Element[list5, 3] + (0, 2))
Poly34, e_3, f_3, g_3, h_3 = Polygon(Element[list7, 3], Element[list7, 3] + (4, 0), Element[list7, 3] + (4, 2), Element[list7, 3] + (0, 2))
Poly35, i_3, j_3, k_3, l_3 = Polygon(Element[list9, 3], Element[list9, 3] + (4, 0), Element[list9, 3] + (4, 2), Element[list9, 3] + (0, 2))
Poly36, m_3, n_3, p_3, q_3 = Polygon(Element[list11, 3], Element[list11, 3] + (4, 0), Element[list11, 3] + (4, 2), Element[list11, 3] + (0, 2))
Poly41, r_3, s_3, t_3, a_4 = Polygon(Element[list1, 4], Element[list1, 4] + (4, 0), Element[list1, 4] + (4, 2), Element[list1, 4] + (0, 2))
Poly42, b_4, c_4, d_4, e_4 = Polygon(Element[list3, 4], Element[list3, 4] + (4, 0), Element[list3, 4] + (4, 2), Element[list3, 4] + (0, 2))
Poly43, f_4, g_4, h_4, i_4 = Polygon(Element[list5, 4], Element[list5, 4] + (4, 0), Element[list5, 4] + (4, 2), Element[list5, 4] + (0, 2))
Poly44, j_4, k_4, l_4, m_4 = Polygon(Element[list7, 4], Element[list7, 4] + (4, 0), Element[list7, 4] + (4, 2), Element[list7, 4] + (0, 2))
Poly45, n_4, p_4, q_4, r_4 = Polygon(Element[list9, 4], Element[list9, 4] + (4, 0), Element[list9, 4] + (4, 2), Element[list9, 4] + (0, 2))
Poly46, s_4, t_4, a_5, b_5 = Polygon(Element[list11, 4], Element[list11, 4] + (4, 0), Element[list11, 4] + (4, 2), Element[list11, 4] + (0, 2))
Poly51, c_5, d_5, e_5, f_5 = Polygon(Element[list1, 5], Element[list1, 5] + (4, 0), Element[list1, 5] + (4, 2), Element[list1, 5] + (0, 2))
Poly52, g_5, h_5, i_5, j_5 = Polygon(Element[list3, 5], Element[list3, 5] + (4, 0), Element[list3, 5] + (4, 2), Element[list3, 5] + (0, 2))
Poly53, k_5, l_5, m_5, n_5 = Polygon(Element[list5, 5], Element[list5, 5] + (4, 0), Element[list5, 5] + (4, 2), Element[list5, 5] + (0, 2))
Poly54, p_5, q_5, r_5, s_5 = Polygon(Element[list7, 5], Element[list7, 5] + (4, 0), Element[list7, 5] + (4, 2), Element[list7, 5] + (0, 2))
Poly55, t_5, a_6, b_6, c_6 = Polygon(Element[list9, 5], Element[list9, 5] + (4, 0), Element[list9, 5] + (4, 2), Element[list9, 5] + (0, 2))
Poly56, d_6, e_6, f_6, g_6 = Polygon(Element[list11, 5], Element[list11, 5] + (4, 0), Element[list11, 5] + (4, 2), Element[list11, 5] + (0, 2))
Poly61, h_6, i_6, j_6, k_6 = Polygon(Element[list1, 6], Element[list1, 6] + (4, 0), Element[list1, 6] + (4, 2), Element[list1, 6] + (0, 2))
Poly62, l_6, m_6, n_6, p_6 = Polygon(Element[list3, 6], Element[list3, 6] + (4, 0), Element[list3, 6] + (4, 2), Element[list3, 6] + (0, 2))
Poly63, q_6, r_6, s_6, t_6 = Polygon(Element[list5, 6], Element[list5, 6] + (4, 0), Element[list5, 6] + (4, 2), Element[list5, 6] + (0, 2))
Poly64, a_7, b_7, c_7, d_7 = Polygon(Element[list7, 6], Element[list7, 6] + (4, 0), Element[list7, 6] + (4, 2), Element[list7, 6] + (0, 2))
Poly65, e_7, f_7, g_7, h_7 = Polygon(Element[list9, 6], Element[list9, 6] + (4, 0), Element[list9, 6] + (4, 2), Element[list9, 6] + (0, 2))
Poly66, i_7, j_7, k_7, l_7 = Polygon(Element[list11, 6], Element[list11, 6] + (4, 0), Element[list11, 6] + (4, 2), Element[list11, 6] + (0, 2))
text5: "$有\;" + (LaTeX[If[s ≟ 0, "n", If[s ≟ 5, "6"]]]) + "\;類不同物品，\;每類至少有\;" + (LaTeX[If[s ≟ 0, "m", If[s ≟ 5, "2"]]]) + "\;件，$
$若由其中每次選取\;" + (LaTeX[If[s ≟ 0, "m", If[s ≟ 5, "2"]]]) + "\;件為一組$
$(不論先後順序)，\;且每組的物品可不$
$盡相異，\;這種組合稱為重複組合，\;而其$
$選取的方法數以 C^{" + (LaTeX[If[s ≟ 0, "n+m-1", If[s ≟ 5, "6+2-1"]]]) + "}_{" + (LaTeX[If[s ≟ 0, "m", If[s ≟ 5, "2"]]]) + "}表之.$"