{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

e511k

# e511k - MAD 2104 Quiz 5 Key Prof S Hudson 1[30pts How many...

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

e511k - MAD 2104 Quiz 5 Key Prof S Hudson 1[30pts How many...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online