Unformatted text preview: them 16 times, every trio eight times, every foursome four times, each set of ±ve twice, and each set of six once, but never all seven at once. If she has lunch every day during the 84 days of the conference, did she ever have lunch alone? [5] 4. How many derangements of 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 are there that (a) start with with 1 , 2 , 3 in some order? [2] (b) end with 4 , 5 , 6 , 7 in some order? [2] (c) start with with 1 , 2 , 3 in some order and end with 4 , 5 , 6 , 7 in some order? [2] 5. Let a n denote the number of ndigit numbers, each of whose digits is 1 , 2 , 3, or 4 and in which the number of 1’s is even. (a) Find a recurrence equation for a n . [3] (b) Find an explicit formula for a n . [3]...
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 Spring '11
 HuangJing
 Integers, ﬁrst midterm test, Professor J

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