L02_MoreCounting

L02_MoreCounting - 1-1COMP170Discrete Mathematical Toolsfor...

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Unformatted text preview: 1-1COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 1.2, pp. 9-19More CountingVersion 2.0: Last updated, JUL 19, 2007Slidesc2005 by M. J. Golin and G. Trippen2-11.2 Counting Lists,Permutations, and Subsets•Using the Sum and Product Principles•Lists and Functions•The Bijection Principle•k-Element Permutations of a Set•k-Element Subsets of a SetBinomial Coefficients3-1Some Simple Examples•The entry code to our office is 4 characters long whereeach character is a number between{...9}.e.g.,1012,2561.How many door codes are there?3-2Some Simple Examples•The entry code to our office is 4 characters long whereeach character is a number between{...9}.e.g.,1012,2561.How many door codes are there?•A computer system’s pasword must be 6 characters long,where each character is in{a...z,A...Z}.e.g.,abcdEF, DHrsAQ, Mickey.How many passwords are there?3-3Some Simple Examples•Hong Kong car plates are of the formL1L2D1D2D3D4where theLiare letters in{A...Z}and theDiare digits in{,...9}.e.g.,AB1234, EC1357.How many car plates are there?•The entry code to our office is 4 characters long whereeach character is a number between{...9}.e.g.,1012,2561.How many door codes are there?•A computer system’s pasword must be 6 characters long,where each character is in{a...z,A...Z}.e.g.,abcdEF, DHrsAQ, Mickey.How many passwords are there?4-1The entry code to our office is 4 characters longwhere each character is a number between{...9}.E.G.,1012,2561.How many door codes are there?4-2The entry code to our office is 4 characters longwhere each character is a number between{...9}.E.G.,1012,2561.How many door codes are there?A door code is of the formX1X2X3X4where,fori= 1,2,3,4,Xi∈ {,1,...,9}(∈meansis inoris a member of)4-3The entry code to our office is 4 characters longwhere each character is a number between{...9}.E.G.,1012,2561.How many door codes are there?A door code is of the formX1X2X3X4where,fori= 1,2,3,4,Xi∈ {,1,...,9}(∈meansis inoris a member of)There are10 possibilities forX110 possibilities forX210 possibilities forX310 possibilities forX4⇒10×10×10×10 = 104= 10,000possible door codes.4-4The entry code to our office is 4 characters longwhere each character is a number between{...9}.E.G.,1012,2561.How many door codes are there?A door code is of the formX1X2X3X4where,fori= 1,2,3,4,Xi∈ {,1,...,9}(∈meansis inoris a member of)There are10 possibilities forX110 possibilities forX210 possibilities forX310 possibilities forX4⇒10×10×10×10 = 104= 10,000possible door codes.Note; This is really theproduct principleWhat are the sets being used?5-1A computer system’s pasword must be 6 characters long,where each character is in{a...z,A...Z}....
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This note was uploaded on 08/25/2010 for the course COMP COMP170 taught by Professor M.j.golin during the Spring '10 term at HKUST.

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L02_MoreCounting - 1-1COMP170Discrete Mathematical Toolsfor...

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