# hw07 - (c increasing digits(d increasing or decreasing...

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In the Name of God Fall 2005 Discrete Mathematics Homework 7 Due: Azar 6 Problem 1. How many n - words from the alphabet { 0 , 1 , 2 } are such that neighbors di±er at most by 1? Problem 2. Of 3 n + 1 objects, n are indistinguishable, and the remaining ones are distinct. Show that one can choose from them n objects in 2 2 n ways. Problem 3. Let f ( n ) be the number of n - words without neighboring zeros from the alphabet { 0 , 1 , 2 } . Find a recursion and a formula for f ( n ). Problem 4. How many 5-words from the alphabet { 0 , 1 , · · · , 9 } have (a) strictly increasing digits, (b) strictly increasing or decreasing digits,
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Unformatted text preview: (c) increasing digits, (d) increasing or decreasing digits? Problem 5. Consider a row of n seats. A child sits on each. Each child may move by at most one seat. Find the number F n of ways they can rearrange. Problem 6. How many subsets of { 1 , 2 , · · · , n } have no two successive num-bers? Problem 7. Let b (0) = 1 and b ( n ) =number of partitions of n into powers of 2 for n ≥ 1. Find recursions for b ( n ). 1...
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