222m2-practice - 201001 Math 222 Midterm 2 Practice...

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201001 Math 222 Midterm 2 Practice Questions 1. How many Social Insurance Numbers (9 digit sequences) have each of the digits 1, 2, 3 and 4 appearing at least once? 2. How many ways are there to arrange the n integers 1 , 2 ,...,n in a circle so that i is never immediately followed by i + 1 and n is never immedi- ately followed by 1? Arrangements that differ by rotating the circle are considered to be the same. 3. A group of 10 people agree to participate in a head-shaving fundraiser. In how many ways can they line up for a “before” shaving photo and (later) an “after” shaving photo if no person occupies the same place in both photos? 4. Find a recurrence relation and initial conditions for a n , the number of se- quences of length n 0 with elements from { A,B,C,D,E } which contain none of AA,AB and BB . 5. Find and solve a recurrence relation and initial conditions for s n , the number of sequences of length n 0 with elements from { a,b,c, 1 , 2 , 3 , 4 } in which there are no consecutive numbers (identical or distinct).
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