MATC44 2008 - s2 - University of Toronto at Scarborough Department of Computer and Mathematical Sciences MAT C44 Winter 2008 Solutions to Assignment#2

MATC44 2008 - s2 - University of Toronto at Scarborough...

This preview shows page 1 - 3 out of 4 pages.

University of Toronto at Scarborough Department of Computer and Mathematical Sciences MAT C44, Winter 2008 Solutions to Assignment #2 Problem 23. on page 155: The student needs to cross 24 intersections on her way to school. On each intersection, she has a choice to go to east or to north, but in total she can go only 10 times to east and 14 times to north. (a) There are ( 24 10 ) ways to decide on what intersections she will go to east. On the remaining intersection, she needs to go to north. Hence, she has ( 24 10 ) different ways to school. (b) She needs to cross 9 intersections to get to her friend’s house. Therefore, she has ( 9 4 ) ways to choose on what intersections she will go east, and on remaining she needs to go north. Similarly, there are ( 15 6 ) different ways to get to school from her friend’s house. Therefore, there are ( 9 4 )( 15 6 ) = 15! 4!5!6! different ways from her house to school if she stops at her friend’s house. (c) If they stop in park, they have ( 9 4 )( 9 3 )( 6 3 ) = (9!) 2 (3!) 3 4!5! different ways to school. (d) Since there are ( 9 4 )( 15 6 ) different ways for two of them to get to school together, and ( 9 4 )( 9 3 )( 6 3 ) ways to get to school if they stop in park, there are ( 9 4 )( 15 6 ) - ( 9 4 )( 9 3 )( 6 3 ) ways for two of them to get to school without crossing the intersection where park is. Problem 26. on page 156: 2 n n + 1 + 2 n n = (2 n )! ( n + 1)!( n - 1)! + (2 n )! n ! n ! = = (2 n )! ( n - 1)! n ! 1 n + 1 + 1 n = (2 n )!(2 n + 1) n !( n + 1)! = 2 n + 1 n On the other hand, 1 2 2 n + 2 n + 1 = 1 2 (2 n + 1)! · 2 · ( n + 1) ( n + 1)!( n + 1)! = (2 n + 1)! n !( n + 1)! = 2 n + 1 n . Hence, 2 n n + 1 + 2 n n = 1 2 2 n + 2 n + 1 . Problem 6. on page 200: Let S be the set of all possible packages of 12 chocolate, cinnamon and plain doughnuts. Let A 1 be the set of all 12-doughnuts packs with more than or equal to 7 chocolate doughnuts. Let A 2 be the set of all 12-doughnuts packs with more than or equal to 7 1
Image of page 1
cinnamon doughnuts. Finally, let
Image of page 2
Image of page 3

You've reached the end of your free preview.

Want to read all 4 pages?

  • Fall '08
  • Math, Combinatorics, SEPTA Regional Rail, Jaguar Racing, ways, Rooks, non attacking rooks

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors