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THE DOCTRINE OF CHANCES. 9 





Corollary.
All the points equally distant from the extremes, that is, from the least and greatest number of points that are upon the dice, have the same number of chances by which they may be produced; wherefore, if the number of points given be nearer to the greater extreme than to the less, let the number of points given be subtracted from the sum of the extremes, and work with the remainder, and the operation will be shortened.
Thus, if it be required to find the number of 
