Graphics3D[{
Blue,Polygon[{{0,0,0},{1,0,0},{1,1,0},{0,1,0}}],
Red,Polygon[{{0,0,0},{1,1,1},{0,1,0}}],Polygon[{{0,0,0},{1,1,1},{1,0,0}}],
Yellow,Polygon[{{0,1,0},{1,1,0},{1,1,1}}],Polygon[{{1,0,0},{1,1,0},{1,1,1}}]
}, Axes->True]

Graphics3D[{
Plot3D[x y, {x,0,1}, {y,0,1}][[1]],
Opacity[.1],
Blue,Polygon[{{0,0,0},{1,0,0},{1,1,0},{0,1,0}}],
Red,Polygon[{{0,0,0},{1,1,1},{0,1,0}}],Polygon[{{0,0,0},{1,1,1},{1,0,0}}],
Yellow,Polygon[{{0,1,0},{1,1,0},{1,1,1}}],Polygon[{{1,0,0},{1,1,0},{1,1,1}}]
},Axes->True]

Manipulate[
Graphics3D[
{If[seeSurface,{ Opacity[.8],Plot3D[x y, {x,0,1}, {y,0,1}][[1]]}],
If[seeSurface,Opacity[.5], Opacity[1]],
Blue,Polygon[{{0,0,0},{1,0,0},{1,1,0},{0,1,0}}],
Red,Polygon[{{0,0,0},{1,1,1},{0,1,0}}],Polygon[{{0,0,0},{1,1,1},{1,0,0}}],
Yellow,Polygon[{{0,1,0},{1,1,0},{1,1,1}}],Polygon[{{1,0,0},{1,1,0},{1,1,1}}],
{Opacity[1],If[z<Min[x,y],Brown,Red], Sphere[{x,y,z}, .01]}
}],
{x,0,1},{y,0,1},{z,0,1}, {seeSurface, {False, True}}]

(* Problem of the fish *)

PA=Binomial[40,2]Binomial[65,6]/Binomial[105,8]

PB=1-(Binomial[40,8]/Binomial[105,8])-(Binomial[40,7]Binomial[65,1]/Binomial[105,8])-(Binomial[40,6]Binomial[65,2]/Binomial[105,8])

(65823272/68087635)

PA/PB

N[PA/PB]

(* Problem of the cards *)

Sum[Binomial[38, k] k! (51-k)!, {k, 0, 38}]/52!