{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

184a_05f_fe

184a_05f_fe - Math 184A Final Exam(80 points 8AM 7 Dec 2005...

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

View Full Document Right Arrow Icon
Math 184A Final Exam (80 points) 8AM 7 Dec. 2005 Please put your name and ID number on your blue book. CLOSED BOOK except for BOTH SIDES of one page of notes. Calculators are NOT allowed. You must show your work to receive credit. 1. (16 pts.) A square table has two seats on each side for a total of eight seats. Rotations of the table don’t matter. Thus, if 1 , 2 , . . ., 8 are placed around the table, 1 2 8 3 7 4 6 5 and 7 8 6 1 5 2 4 3 are the same, but di±er from 2 1 3 8 4 7 5 6 and 8 1 7 2 6 3 5 4 . (a) How many ways can eight people be seated at the table? (b) We have four identical red chairs and four identical blue chairs. How many ways can the eight chairs be placed around the table? Again, rotations of the table do not matter. 2. (18 pts.) Let V = { 1 , 2 , . . ., n } . (a) Compute the number of simple graphs with vertex set V that have exactly q edges. (b) A vertex is isolated if it does not lie on any edges. Suppose S V . Compute the number of simple graphs with vertex set
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

184a_05f_fe - Math 184A Final Exam(80 points 8AM 7 Dec 2005...

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

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online