在A,B,C,D,E\;這5個人中，\;選取3人排成一列，\;試求方法數。\

考慮被選中的人底下畫◯沒被選中的人畫×

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組合(1)

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s = 0 (slider from 0 to 22, step 1)
text2: "P^5_3=5×4×3=60\;\;或乘法原理：\;5×4×3=60\\
\fgcolor{white}{" + (LaTeX[If[s ≥ 3, "若題目改為從上述5人中任取3人為一組，求方法數。"]]) + "}
\\" + (LaTeX[If[s ≥ 4, "因為3個人排成一列的排列數為3!\;⇒\frac{60}{3!}=10"]]) + "\\" + (LaTeX[If[s ≥ 5, "為了方便，\;我們選定符號C^5_3代表\frac{5×4×3}{3×2×1}"]]) + "\\" + (LaTeX[If[s ≥ 6, "由n個相異物中任取r個為一組的方法數為：\\C^n_r=\frac{P^n_r}{r!}=\frac{n×(n-1)×(n-2)×...×(n-r+1)}{r×(r-1)×...×3×2×1}"]]) + ""
A = (0.4063603636832763, -3.8428389829711427)
list1 = Sequence(Segment[A + ((6 * k), 10), A + ((6 * k), (-2))], k, 0, 5)
a_1 = Segment(A + (0, 10), A + (30, 10))
a_2 = Segment(A, A + (30, 0))
a_3 = Segment(A + (0, (-2)), A + (30, (-2)))
B = (2.195747071237088, -3.731571296238005)
B_1: A + (1.1, 0)
B_2: A + (7.5, 0)
B_3: A + (13.2, 0)
B_4: A + (19, 0)
B_5: A + (25.5, 0)
text9: "◯◯◯××\;\;\;\;\;" + (LaTeX[If[s ≥ 15, "◯××◯◯"]]) + "\\" + (LaTeX[If[s ≥ 11, "◯◯×◯×"]]) + "\;\;\;\;\;" + (LaTeX[If[s ≥ 16, "×◯◯◯×"]]) + "\\" + (LaTeX[If[s ≥ 12, "◯◯××◯"]]) + "\;\;\;\;\;" + (LaTeX[If[s ≥ 17, "×◯◯×◯"]]) + "\\" + (LaTeX[If[s ≥ 13, "◯×◯◯×"]]) + "\;\;\;\;\;" + (LaTeX[If[s ≥ 18, "×◯×◯◯"]]) + "\\" + (LaTeX[If[s ≥ 14, "◯×◯×◯"]]) + "\;\;\;\;\;" + (LaTeX[If[s ≥ 19, "××◯◯◯"]]) + ""
text10: "所求即3個◯與2個×的直線排列數\frac{5!}{3!×2!}=10\\" + (LaTeX[If[s ≥ 21, "而且：\;C^5_3=C^5_2"]]) + "" + (LaTeX[If[s ≥ 22, "，\;也就是說：\;C^n_r=C^n_{n-r}，\\當n,r為非負整數且n≥r"]]) + ""
C = (3.724181550605969, -3.731571296238005)
D = (9.804318728959693, -3.8428389829711427)
E = (15.897515953311453, -3.8428389829711427)
F = (22.23302596097779, -3.8428389829711427)
G = (29.20227709423611, -3.8428389829711427)
poly1, a, b, c, d = Polygon(A, A + (30, 0), A + (30, 10), A + (0, 10))