Date: 18 2 月 2013

$ 重複組合 $

$k=%v$

$n=%v$

$Step=%v$

(1,0)

(0,1)

(1,0,0)

(0,1,0)

(0,0,1)

(1,0,0,0)

(0,1,0,0)

(0,0,1,0)

(0,0,0,1)

(2,0)

(1,1)

(0,2)

(2,0,0)

(0,2,0)

(0,0,2)

(1,1,0)

(1,0,1)

(0,1,1)

(2,0,0,0)

(0,2,0,0)

(0,0,2,0)

(0,0,0,2)

(1,1,0,0)

(1,0,1,0)

(1,0,0,1)

(0,1,1,0)

(0,1,0,1)

(0,0,1,1)

(3,0)

(2,1)

(1,2)

(0,3)

(3,0,0)

(0,3,0)

(0,0,3)

(2,1,0)

(2,0,1)

(1,2,0)

(1,0,2)

(0,1,2)

(0,2,1)

(1,1,1)

(3,0,0,0)

(0,3,0,0)

(0,0,3,0)

(0,0,0,3)

(2,1,0,0)

(2,0,1,0)

(2,0,0,1)

(1,2,0,0)

(1,0,2,0)

(1,0,0,2)

(0,2,1,0)

(0,2,0,1)

(0,1,2,0)

(0,1,0,2)

(0,0,2,1)

(0,0,1,2)

(1,1,1,0)

(1,1,0,1)

(1,0,1,1)

(0,1,1,1)

(4,0)

(3,1)

(2,2)

(1,3)

(0,4)

(4,0,0)

(0,4,0)

(0,0,4)

(3,1,0)

(3,0,1)

(1,3,0)

(1,0,3)

(0,3,1)

(0,1,3)

(2,2,0)

(2,0,2)

(0,2,2)

(2,1,1)

(1,2,1)

(1,1,2)

(4,0,0,0)

(0,4,0,0)

(0,0,4,0)

(0,0,0,4)

(3,1,0,0)

(3,0,1,0)

(3,0,0,1)

(1,3,0,0)

(1,0,3,0)

(1,0,0,3)

(0,3,1,0)

(0,3,0,1)

(0,1,3,0)

(0,1,0,3)

(0,0,3,1)

(0,0,1,3)

(2,2,0,0)

(2,0,2,0)

(2,0,0,2)

(0,2,2,0)

(0,2,0,2)

(0,0,2,2)

(2,1,1,0)

(2,1,0,1)

(2,0,1,1)

(1,2,1,0)

(1,2,0,1)

(1,1,2,0)

(1,1,0,2)

(1,0,2,1)

(1,0,1,2)

(0,2,1,1)

(0,1,2,1)

(0,1,1,2)

(1,1,1,1)

1

顯示答案

k = 1 (slider from 1 to 4, step 1)
n = 2 (slider from 2 to 4, step 1)
s = 0 (slider from 0 to If[k ≟ 1 ∧ n ≟ 1, 1, If[k ≟ 1 ∧ n ≟ 2, 2, If[k ≟ 1 ∧ n ≟ 3, 3, If[k ≟ 1 ∧ n ≟ 4, 4, If[k ≟ 2 ∧ n ≟ 1, 1, If[k ≟ 2 ∧ n ≟ 2, 3, If[k ≟ 2 ∧ n ≟ 3, 6, If[k ≟ 2 ∧ n ≟ 4, 10, If[k ≟ 3 ∧ n ≟ 1, 1, If[k ≟ 3 ∧ n ≟ 2, 4, If[k ≟ 3 ∧ n ≟ 3, 10, If[k ≟ 3 ∧ n ≟ 4, 20, If[k ≟ 4 ∧ n ≟ 1, 1, If[k ≟ 4 ∧ n ≟ 2, 5, If[k ≟ 4 ∧ n ≟ 3, 15, If[k ≟ 4 ∧ n ≟ 4, 35]]]]]]]]]]]]]]]], step 1)
A = (-1.9, 4.48)
list1 = Sequence(A + (j, 0), j, 0, 13)
list2 = Sequence(A + (j, -1), j, 0, 13)
list3 = Sequence(A + (j, -2), j, 0, 13)
list4 = Sequence(A + (j, -3), j, 0, 13)
list5 = Sequence(A + (j, -4), j, 0, 13)
list6 = Sequence(A + (j, -5), j, 0, 13)
list7 = Sequence(A + (j, -6), j, 0, 13)
list8 = Sequence(A + (j, -7), j, 0, 13)
list9 = Sequence(A + (j, -8), j, 0, 13)
lista = Sequence(A + (j, -9), j, 0, 13)
poly11 = PolyLine(A, A + (1, 0), A + (1, 1), A + (0, 1), A)
poly12 = PolyLine(A + (0, 1), A + (2, 1), A + (2, -1), A + (0, -1), A + (0, 1))
a_{12} = Segment(A, A + (2, 0))
poly13 = PolyLine(A + (0, 1), A + (3, 1), A + (3, -2), A + (0, -2), A + (0, 1))
a_{131} = Segment(A, A + (3, 0))
a_{132} = Segment(A + (0, -1), A + (3, -1))
poly14 = PolyLine(A + (0, 1), A + (4, 1), A + (4, -3), A + (0, -3), A + (0, 1))
a_{141} = Segment(A, A + (4, 0))
a_{142} = Segment(A - (0, 1), A + (4, -1))
a_{143} = Segment(A - (0, 2), A + (4, -2))
poly21 = PolyLine(A + (0, 1), A + (2, 1), A + (2, 0), A, A + (0, 1))
poly22 = PolyLine(A + (0, 1), A + (3, 1), A + (3, -2), A - (0, 2), A + (0, 1))
a_{221} = Segment(A, A + (3, 0))
a_{222} = Segment(A - (0, 1), A + (3, -1))
poly23 = PolyLine(A + (0, 1), A + (4, 1), A + (4, -5), A - (0, 5), A + (0, 1))
a_{231} = Segment(A, A + (4, 0))
a_{232} = Segment(A - (0, 1), A + (4, -1))
a_{233} = Segment(A - (0, 2), A + (4, -2))
a_{234} = Segment(A - (0, 3), A + (4, -3))
a_{235} = Segment(A - (0, 4), A + (4, -4))
poly24 = PolyLine(A + (0, 1), A + (5, 1), A + (5, -8), A - (0, 8), A + (0, 1))
poly24a = PolyLine(A + (7, 1), A + (12, 1), A + (12, 0), A - (-7, 0), A + (7, 1))
a_{242} = Segment(A - (0, 1), A + (5, -1))
a_{241} = Segment(A, A + (5, 0))
a_{243} = Segment(A - (0, 2), A + (5, -2))
a_{244} = Segment(A - (0, 3), A + (5, -3))
a_{245} = Segment(A - (0, 4), A + (5, -4))
a_{246} = Segment(A - (0, 5), A + (5, -5))
a_{247} = Segment(A - (0, 6), A + (5, -6))
a_{248} = Segment(A - (0, 7), A + (5, -7))
poly31 = PolyLine(A + (0, 1), A + (3, 1), A + (3, 0), A, A + (0, 1))
poly32 = PolyLine(A + (0, 1), A + (4, 1), A + (4, -3), A + (0, -3), A + (0, 1))
a_{322} = Segment(A - (0, 1), A + (4, -1))
a_{323} = Segment(A - (0, 2), A + (4, -2))
a_{321} = Segment(A, A + (4, 0))
poly34 = PolyLine(A + (0, 1), A + (6, 1), A + (6, -9), A - (0, 9), A + (0, 1))
poly34a = PolyLine(A + (7, 1), A + (13, 1), A + (13, -9), A - (-7, 9), A + (7, 1))
a_{341} = Segment(A, A + (6, 0))
a_{342} = Segment(A + (0, -1), A + (6, -1))
a_{343} = Segment(A + (0, -2), A + (6, -2))
a_{344} = Segment(A + (0, -3), A + (6, -3))
a_{345} = Segment(A + (0, -4), A + (6, -4))
a_{346} = Segment(A + (0, -5), A + (6, -5))
a_{347} = Segment(A + (0, -6), A + (6, -6))
a_{348} = Segment(A + (0, -7), A + (6, -7))
a_{349} = Segment(A + (0, -8), A + (6, -8))
a_{34a} = Segment(A + (7, 0), A + (13, 0))
a_{34b} = Segment(A + (7, -1), A + (13, -1))
a_{34c} = Segment(A + (7, -2), A + (13, -2))
a_{34d} = Segment(A + (7, -3), A + (13, -3))
a_{34e} = Segment(A + (7, -4), A + (13, -4))
a_{34f} = Segment(A + (7, -5), A + (13, -5))
a_{34g} = Segment(A + (7, -6), A + (13, -6))
a_{34h} = Segment(A + (7, -7), A + (13, -7))
a_{34i} = Segment(A + (7, -8), A + (13, -8))
poly41 = PolyLine(A + (0, 1), A + (4, 1), A + (4, 0), A, A + (0, 1))
poly42 = PolyLine(A + (0, 1), A + (5, 1), A + (5, -4), A - (0, 4), A + (0, 1))
a_{422} = Segment(A + (0, -1), A + (5, -1))
a_{421} = Segment(A, A + (5, 0))
a_{423} = Segment(A + (0, -2), A + (5, -2))
a_{424} = Segment(A + (0, -3), A + (5, -3))
poly43 = PolyLine(A + (0, 1), A + (6, 1), A + (6, -8), A - (0, 8), A + (0, 1))
poly43a = PolyLine(A + (7, 1), A + (13, 1), A + (13, -5), A - (-7, 5), A + (7, 1))
a_{432} = Segment(A + (0, -1), A + (6, -1))
a_{431} = Segment(A, A + (6, 0))
a_{433} = Segment(A + (0, -2), A + (6, -2))
a_{434} = Segment(A + (0, -3), A + (6, -3))
a_{435} = Segment(A + (0, -4), A + (6, -4))
a_{436} = Segment(A + (0, -5), A + (6, -5))
a_{437} = Segment(A + (0, -6), A + (6, -6))
a_{438} = Segment(A + (0, -7), A + (6, -7))
a_{43b} = Segment(A + (7, -1), A + (13, -1))
a_{43a} = Segment(A + (7, 0), A + (13, 0))
a_{43c} = Segment(A + (7, -2), A + (13, -2))
a_{43d} = Segment(A + (7, -3), A + (13, -3))
a_{43e} = Segment(A + (7, -4), A + (13, -4))
poly44 = PolyLine(A + (0, 1), A + (7, 1), A + (7, -8), A - (0, 8), A + (0, 1))
poly44a = PolyLine(A + (7, 1), A + (14, 1), A + (14, -8), A - (-7, 8), A + (7, 1))
a_{442} = Segment(A + (0, -1), A + (7, -1))
a_{441} = Segment(A, A + (7, 0))
a_{443} = Segment(A + (0, -2), A + (7, -2))
a_{444} = Segment(A + (0, -3), A + (7, -3))
a_{445} = Segment(A + (0, -4), A + (7, -4))
a_{446} = Segment(A + (0, -5), A + (7, -5))
a_{447} = Segment(A + (0, -6), A + (7, -6))
a_{448} = Segment(A + (0, -7), A + (7, -7))
a_{44b} = Segment(A + (7, -1), A + (14, -1))
a_{44c} = Segment(A + (7, -2), A + (14, -2))
a_{44d} = Segment(A + (7, -3), A + (14, -3))
a_{44e} = Segment(A + (7, -4), A + (14, -4))
a_{44f} = Segment(A + (7, -5), A + (14, -5))
a_{44g} = Segment(A + (7, -6), A + (14, -6))
a_{44h} = Segment(A + (7, -7), A + (14, -7))
a_{44a} = Segment(A + (7, 0), A + (14, 0))
a: s - 1
b = true
t1: "$求方程式$
$ x" + (LaTeX[If[n ≥ 2, "+y"]]) + "" + (LaTeX[If[n ≥ 3, "+z"]]) + "" + (LaTeX[If[n ≥ 4, "+u"]]) + "" + (LaTeX[If[n ≥ 5, "+v"]]) + "=" + (LaTeX[k]) + " $
$的非負整數解$"
text2: "$將 " + (LaTeX[k]) + "個相同的球分$
$給 " + (LaTeX[n]) + "個人,求方法數.$"
t2: "$\frac{" + (LaTeX[k + n - 1]) + "!}{" + (LaTeX[k]) + "!×" + (LaTeX[n - 1]) + "!}=C^ " + (LaTeX[k + n - 1]) + "_" + (LaTeX[k]) + " =C^" + (LaTeX[k + n - 1]) + "_" + (LaTeX[n - 1]) + "$
$=C^{" + (LaTeX[n]) + " + " + (LaTeX[k]) + "-1}_ " + (LaTeX[k]) + "=H^" + (LaTeX[n]) + "_" + (LaTeX[k]) + "$
$=" + (LaTeX[Binomial[k + n - 1, k]]) + "$"