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Unformatted text preview: Chapter 5 Summary August 5, 2009 This chapter can be summarized in a table Arrangement (Ordered) Selection (Unordered) Distribution of Distinct Objects Distribution of Identical Objects No Repetition P ( n,r ) C ( n,r ) Unlimited Repetition n r C ( n + r- 1 ,r ) Restricted Repetition P ( n ; r 1 ,r 2 ,...,r m ) About how to check the table 1. Is it an arrangement/selection question or a distribution question? 2. Does the order matter? / Are you dealing with distinct objects or identical objects? • For an arrangement/selection question, you need to think about the order. For example, if you rearrange some letters to get a new word , then the order matters. So you need to look at the left column. If you want to have a 5-card poker hand, then you just care about what you have in your hand. So you need to look at the right column. • For a distribution question, you need to think about whether your objects to distribute are identical or distinct. For example, if you want to distribute cards to players, then you're distributing distinct objects. So you need to look at the left column. Otherwise, see the right one. • Note: see the di erence between selecting a poker hand and distributing cards to players . 3. Are there any repeated objects? If yes, is there any restriction on the repetition? • For an arrangement/selection question, you need to see if there are any repeated objects in your pool . For example, if you want to get a poker hand from a 52-card deck, since all the cards are distinct and nothing is repeated, so the question belongs to no repetition . So you check the rst row.you check the rst row....
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This note was uploaded on 02/13/2011 for the course AMS 301 taught by Professor Arkin during the Spring '08 term at SUNY Stony Brook.
- Spring '08