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Unformatted text preview: form a 4person committee that contains at least one person from each department. How many possible committees are there? You may leave factorials and binomial coecients in your answer. 4. (8 pts.) Describe all permutations f of { 1 , 2 , 3 , 4 , 5 } such that f k is not the identity for any positive k { 1 , 2 , 3 , 4 , 5 } . You must justify your answer. Hint : Look at cycle lengths. 5. (8 pts.) A kpart partition of n is a kmultiset of positive integers whose sum is n . For example the 2part partitions of 6 are { 1 , 5 } , { 2 , 4 } and { 3 , 3 } . (a) Prove that there are exactly m 2part partitions of 2 m when m > 0. (b) State and prove a formula for the number of 2part partitions of 2 m + 1 when m > 0. Hint : If you do not see the formula right away, list the partitions for m = 1, m = 2 and maybe m = 3. END OF EXAM...
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This note was uploaded on 06/18/2009 for the course MATH 184a taught by Professor Staff during the Winter '08 term at UCSD.
 Winter '08
 staff
 Math

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