e511k - MAD 2104 Quiz 5 Key Oct 27, 2011 Prof. S. Hudson 1)...

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MAD 2104 Oct 27, 2011 Quiz 5 Key Prof. S. Hudson 1) [30pts] How many ways can 8 men and 5 women be placed in a line, such that no two women stand next to each other ? Hint: place the men first. 2) [20pts] In class, we proved a theorem about monotone subsequences. Using the notation of that proof, find ( d 3 ,i 3 ) for the sequence 3, 6, 9, 4, 7, 10, 5, 8, 11, 12. 3) [20pts] How many ways can you put 5 eggs into 3 baskets, A, B and C ? 4) [30pt] Choose ONE proof. a) Determine which amounts of postage can be formed from 3 cent and 5 cent stamps. Prove your answer using Strong Induction. b) Give a combinatorial proof [Hint: count committees-with-a-leader two ways] that for all positive integers n , n X k =1 kC ( n,k ) = n 2 n - 1 Remarks and Answers: The average of the top 20 grades was approx 50, and the highest was 70, which suggests this was a relatively hard quiz. The lowest scores were on Problem 1, which (I thought) was a fairly standard counting problem. The unofficial scale is; A’s 65 - 100
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e511k - MAD 2104 Quiz 5 Key Oct 27, 2011 Prof. S. Hudson 1)...

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