lect1 - THE MULTIPLICATION RULE PERMUTATIONS COMBINATIONS...

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THE MULTIPLICATION RULE PERMUTATIONS Introduction to Probability Models Xinghua Zheng 1 1 ISOM, HKUST 1 / 15 Xinghua Zheng Lect 1: Combinatorics
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THE MULTIPLICATION RULE PERMUTATIONS Outline THE MULTIPLICATION RULE PERMUTATIONS COMBINATIONS SOME COMBINATORIAL IDENTITIES SUMMARY 2 / 15 Xinghua Zheng Lect 1: Combinatorics
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THE MULTIPLICATION RULE PERMUTATIONS EXAMPLE: POKER A deck of cards In (five-card draw) poker, you are dealt 5 cards. A hand such as with two cards of one rank, and three cards of another rank, is called a full house . Q: What’s the chance of being dealt a full house? 3 / 15 Xinghua Zheng Lect 1: Combinatorics
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THE MULTIPLICATION RULE PERMUTATIONS EXAMPLE: POKER ( ctd) Assume that all possible poker hands are equally likely , then the chance of being dealt a full house equals p FH := N FH N where N := the number of all possible poker hands N FH := the number of those hands that are a full-house. Q: How to compute N and N FH ? – This lecture develops combinatorial methods to compute N and N FH , and related quantities. 4 / 15 Xinghua Zheng Lect 1: Combinatorics
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THE MULTIPLICATION RULE PERMUTATIONS THE MULTIPLICATION RULE FOR COUNTING Two cards will be drawn without replacement from the following mini-deck Q: If keep track of the order of the cards, how many outcomes are there? The first card can be chosen in ways. Regardless of the choice of the first card, the second card can be chosen in ways. There are × = possible pairs. 5 / 15 Xinghua Zheng Lect 1: Combinatorics
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THE MULTIPLICATION RULE PERMUTATIONS MULTIPLICATION RULE ( ctd) Q: If draw three cards without replacement and keep track of the order, how many possible outcomes are there?
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This note was uploaded on 11/27/2011 for the course ISOM 3540 taught by Professor Zheu during the Spring '11 term at HKUST.

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lect1 - THE MULTIPLICATION RULE PERMUTATIONS COMBINATIONS...

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