MATH 475 Spring 2005 FINAL EXAM
Solutions (in-class part)
1. Fourteen players will be assigned to play poker at three tables: ve at two tables and
four at one table. Two assignments of players will be considered the same if each player
has the same person
MATH 475 Spring 2005
FINAL EXAM SOLUTIONS (take-home part)
1. Let be a random permutation of the set cfw_1, 2, . . . , n. Let pn denote the probability
that has a cycle of length at least n/2.
(a) Compute pn .
(b) Compute limn pn .
(c) Does your formula i
MATH 475 Spring 2005 FINAL EXAM (in-class part)
Each problem is worth 13 points.
1. Fourteen players will be assigned to play poker at three tables: ve at two tables and
four at one table. Two assignments of players will be considered the same if each pla
MATH 475 Spring 2005 FINAL EXAM (take-home part)
INSTRUCTIONS. You may use books (although theyre not necessary), but you may not consult with
other people.
When the answer is a number, compute the number, not only a formula in numbers e.g., from 5! 3!,
c
EXAM 2MATH 475SPRING 2005
No books, notes, calculators or electronic devices.
Write enough that I can understand your reasoning.
1. (15 points) How many ways are there to pick a group of 30 people from 100
people (each of a dierent height) and then pick a
EXAM 1MATH 475SPRING 2005
No books, notes, calculators or electronic devices.
1. (15 pts) A planar graph contains 500 vertices and 8 connected components. The
graph divides the plane into 12 regions (including the one unbounded region).
How many edges are
Math/Cmsc 475, Jeffrey Adams
Final, May 18, 2012
For full credit show all work
Each problem is worth 25 points
1. Find the number of solutions of a + b + c + d = 10 Where a,b,c,d are
integers, satisfying 0 S a, 1 S b, 2 S c, 3 S d.
2. The inversion sequ
MATH 475 Spring 2005 FINAL EXAM
Solutions (in-class part)
1. Fourteen players will be assigned to play poker at three tables: ve at two tables and
four at one table. Two assignments of players will be considered the same if each player
has the same person
MATH 475 Spring 2005
FINAL EXAM SOLUTIONS (take-home part)
1. Let be a random permutation of the set cfw_1, 2, . . . , n. Let pn denote the probability
that has a cycle of length at least n/2.
(a) Compute pn .
(b) Compute limn pn .
(c) Does your formula i
MATH 475 Spring 2005 FINAL EXAM (in-class part)
Each problem is worth 13 points.
1. Fourteen players will be assigned to play poker at three tables: ve at two tables and
four at one table. Two assignments of players will be considered the same if each pla
MATH 475 Spring 2005 FINAL EXAM (take-home part)
INSTRUCTIONS. You may use books (although theyre not necessary), but you may not consult with
other people.
When the answer is a number, compute the number, not only a formula in numbers e.g., from 5! 3!,
c
EXAM 2 SOLUTIONS MATH 475 SPRING 2005
.
PROBLEM 1.
How many ways are there to pick a group of 30 people from 100 people (each of
a dierent height) and then pick a second group of 25 other people such that all
people in the rst group are taller than the pe
EXAM 1 SOLUTIONS MATH 475 SPRING 2005
.
PROBLEM 1
A planar graph contains 500 vertices and 8 connected components. The graph
divides the plane into 12 regions (including the one unbounded region).
How many edges are in the graph?
SOLUTION
For a connected
EXAM 2MATH 475SPRING 2005
No books, notes, calculators or electronic devices.
Write enough that I can understand your reasoning.
1. (15 points) How many ways are there to pick a group of 30 people from 100
people (each of a dierent height) and then pick a
EXAM 1MATH 475SPRING 2005
No books, notes, calculators or electronic devices.
1. (15 pts) A planar graph contains 500 vertices and 8 connected components. The
graph divides the plane into 12 regions (including the one unbounded region).
How many edges are