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COUNTING1
Problems we want to solveHow many ways are there to seat four peoplearound a circular table, where two seatingsare considered the same when each personhas the same left and right neighbor?How many cards must Bob selectfrom a standard deck of 52 cards toguarantee that at least three cardsof the same suit are chosen?Alice likes 4 types of bagels. Howmany ways are there to select adozen bagels when she choosesonly among the 4 types she likes?2
BASICS OF COUNTING(6.1)Basic Counting Principles andCounting Rules3
Counting RulesProduct RuleSum RuleSubtraction RuleDivision Rule4
The Product RuleExample: How many bit strings of length seven arethere?
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Example: License PlatesHow many different license plates can be made if eachplate is a sequence of three uppercase English lettersfollowed by three digits?e.g., AGF349Solution:By the product rule, there are262626∙ 10 ∙ 10 ∙ 10 = 17,576,000different possible license plates.6
Example: Telephone Numbering PlanTheNorth American Numbering Plan(NANP) specifiesthat a telephone number consists of 10 digits:3-digit area code, 3-digit office code, a 4-digit station code.There are some restrictions on the digits.LetXdenote a digit from 0 through 9.LetNdenote a digit from 2 through 9.LetYdenote a digit that is 0 or 1.Format in old plan (used in 1960s):NYX-NNX-XXXX.Format in new plan:NXX-NXX-XXXX.How many different telephone numbers are possible underthe old plan and the new plan?7
X= {0, …, 9},N= { 2, …, 9},Y= {0, 1}old plan format:NYX-NNX-XXXXnew plan format:NXX-NXX-XXXXHow many different telephone numbers arepossible?8
X= {0, …, 9},N= { 2, …, 9},Y= {0, 1}old plan format:NYX-NNX-XXXXnew plan format:NXX-NXX-XXXXHow many different telephone numbers arepossible?
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Term
Spring
Professor
AbhinavDangeti
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