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Unformatted text preview: ( 16 11 ) . 12. 10626. 17. 2520. 18. 20! 4!(3!) 3 (2!) 3 . 20. 364. 21. ( 14 6 ) . 23. 12! (2!) 6 . 24. If you assume that the ﬁrst box has 1 object, the second one 2, etc., then the number of ways to distribute the objects is 15! 1!2!3!4!5! . However, the way the question is phrased, it only seems to say one of the boxes (not necessarily the ﬁrst) has 1 object, some other box has 2 objects, etc. and in this case the number of ways to distribute the objects is 5!15! 1!2!3!4!5! . 25. ( 24 19 )6 ( 14 9 ) . 26. 6 ( 8 4 ) . 32. 6! 2! . 33. 63. 34. 7! 3!3! + 6! 3!3! + 2 · 6! 3!2! + 2 · 5! 3! + ! 2!2! + 2 · 5! 3!2! = 370. 38. a) 40! (10!) 4 . b) 40! 4!(10!) 4 . 39. 12! 4!3!5! . 42. 52! 13! 4 . 48. Observe that we do not consider the ordering of the elements inside the boxes, and hence they can be treated as indistinguishable. 2...
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 Fall '12
 Gupta
 Math, Harshad number, Prime number, mutual friends, mutual enemies

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