quiz5_solutions

# quiz5_solutions - b n-1 2 n-1 This gives a = 1,b =-1 2 How...

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University of California, Santa Barbara CMPSC 40 SUMMER 2009 QUIZ V N A M E : 1. Let a n denote the number of regions into which the plane is divided when we draw n ovals so that any two intersect in exactly two points and no three intersect at a point. (a) Write down a recursion satisFed by the a n . As was done in class, for n 2 , a n = a n - 1 + 2( n - 1) . (b) ±ind a particular solution a p n to this recursion. Try n ( an + b ) . Then an 2 + bn = a ( n - 1) 2 +
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Unformatted text preview: b ( n-1) + 2( n-1) . This gives a = 1 ,b =-1 . 2. How many strings of four decimal digits (a) do not contain the same digit three times? 10 4-10 × 9 × p 4 3 P (b) begin with an odd digit? 5 × 10 3 (c) have exactly two digits that are 4s? p 4 2 P × 9 2 3. How many permutations of the letters ABCDEFG contain the string CFGA ? Show your work. p 4 1 P × 3!...
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