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Now we consider a "box" with two white marbles and two black marbles inside it. The box is made so that exactly two of the marbles are always on the left hand side and two are always on the right hand side of the box. In the case shown to the right, both white marbles are on the left side of the box and both black marbles are on the right side of the box. There is only one combinations of marbles that gives this arrangement. Imagine that we shake the box, and how the marbles distribute themselves is random. Now we have a white marble and a black marble on the left, and a white and black marble on the right. Call the black marbles B1 and B2, and the white ones W1 and W2. Then for this arrangement we could have B1,W1 on the left and B2,W2 on the right. We could also have B1,W2 on the left and B2,W1 on the right; or B2W1 on the left and B1,W2 on the right; or B2,W2 on the left and B1,W1 on the right. Thus there are four combinations that give this arrangement of the marbles. Finally, we show the single arrangement with both black marbles on the left and both white ones on the right.


20. May 2010 08:13:52 EDT
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