Physics 404 Problem Set #1 (80 points total) Due Sept 16, 2008 A note on how points are tallied in homework problems: Each problem is worth 10 points, unless otherwise noted. At the end of the semester we will drop 9 of your lowest scored problems, add up the points for all the remaining problems and adjust the score to have a maximum of 200 (note 20% of your total course score comes from homework) 1. (worth 20 points) We discussed in class the different ways of placing 4 colored balls in two partitions (with one divider) of equal volume v, and calculated the multiplicity functions for each arrangement (e.g., 1 ball on the left, 3 balls on the right, etc) . a) Now generalize this to three partitions (with two dividers). I, II, III. Show the different spatial arrangements with i) one ball ii) two distinguishable balls and iii) three distinguishable balls. (6 points) b) Further generalizing the case with 4 partitions (assuming each has the same volume v). Show the different spatial arrangements with
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