lec16-counting - EECS 203, Winter 2007 Discrete Mathematics...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
EECS 203, Winter 2007 Discrete Mathematics Lecture 16 Basic counting; Inclusion-Exclusion Principle; Pigeonhole Principle March 6 Reading: Rosen [5.1, 5.2] March 6 Basic counting; Inclusion-Exclusion Principle; Pigeonhole Principle, Page 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
16.1 Basic counting principles Two simple formulas If A = A 1 × A 2 × ··· A m , then | A | = Π m i =1 | A i | . If A = A 1 A 2 ∪ ··· ∪ A m and A i A j = ϕ , for all i 6 = j , then | A | = m X i =1 | A i | . Use them to do counting: The Product Rule: if a task can be decomposed into m steps, each step has n i options, i = 1 ,...,m then the total number of options for completing the task is Π m i =1 n i . The Sum Rule: if a task can be accomplished in one of n 1 ways, or, one of n 2 ways, or, . .., one of n m ways, and no pair of those ways are the same, then there are in total n 1 + ··· + n m March 6 Basic counting; Inclusion-Exclusion Principle; Pigeonhole Principle, Page 2
Background image of page 2
ways to accomplish the task. March 6
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/01/2008 for the course EECS 203 taught by Professor Yaoyunshi during the Winter '07 term at University of Michigan.

Page1 / 7

lec16-counting - EECS 203, Winter 2007 Discrete Mathematics...

This preview shows document pages 1 - 4. Sign up to view the full document.

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