# CS336f1016 - 11/8/10 Example

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Unformatted text preview: 11/8/10 Example  How many ways are there of arranging 6 people  at a round table?  How many ways are there of arranging six  people at a round table so that Romeo and  Juliet are sitting next to one another but  Ceasar and Brutis are not?  Example  •  How   many   ways   can   we   order   the   letters   in  MISSISSIPPI where all four I’s are not together?    How is this different from past problems?  Example  How many ways can you roll a pair of red dice?  Example  How many ways can you roll a pair of red dice?  11 12 22 13 23 33 14 24 34 44 15 25 35 45 55 16 26 36 46 56 66 Table  Our questions:  order replacement yes no yes no Example  How many ways can you place two balls in three  boxes?  Product rule Permutation ? Combination 1 11/8/10 Example  How many ways can you place two balls in three  boxes?  1 1 1 1 1 1 2 2 2 Example  How many ways can you place two balls in  three boxes?  1 1 1 1 1 2 2 2 *|*|        **||  *||*        |**|  1 |*|*        ||**  Example  How many ways can you place two balls in  three boxes?  How many ways can we  choose places for two balls and two  transitions”  C(4,2)=6  *|*|        **||  *||*        |**|  |*|*        ||**  Our questions:  order replacement yes no Table  Yes Product rule Product rule P(n,r) No Combination C(n+r-1,r) C(n,r) Example    A   bagel   shop   has   onion   bagels,   poppy   seed  bagels,   egg   bagels,   pumpernickel   bagels,   salty  bagels,   sesame   seed   bagels,   raisin   bagels,   and  plain bagels.    •  How   many   ways   are   there   of   choosing   six  bagels?  Example    A bagel shop has onion bagels, poppy seed  bagels, egg bagels, pumpernickel bagels, salty  bagels, sesame seed bagels, raisin bagels, and  plain bagels.    •  How many ways are there of choosing a dozen  bagels?  2 11/8/10 Example    A bagel shop has onion bagels, poppy seed  bagels, egg bagels, pumpernickel bagels, salty  bagels, sesame seed bagels, raisin bagels, and  plain bagels.    •  How many ways are there of choosing a dozen  bagels with at least one of each kind?  Example    A bagel shop has onion bagels, poppy seed  bagels, egg bagels, pumpernickel bagels, salty  bagels, sesame seed bagels, raisin bagels, and  plain bagels.    •  How many ways are there of choosing a dozen  bagels with at least 3 plain?  Example    A bagel shop has onion bagels, poppy seed  bagels, egg bagels, pumpernickel bagels, salty  bagels, sesame seed bagels, raisin bagels, and  plain bagels.    •  How many ways are there of choosing a dozen  bagels with less than 3 plain?  Example    A bagel shop has onion bagels, poppy seed bagels,  egg bagels, pumpernickel bagels, salty bagels,  sesame seed bagels, raisin bagels, and plain bagels.    •  How many ways are there of choosing a dozen bagels  with at least 3 plain and no more than 2 onion?  Example  •  How many positive numbers less than 1000  have at least one digit equal 9 and the sum of  the digits equal 13.  3 ...
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## This note was uploaded on 11/30/2010 for the course CS 336 taught by Professor Myers during the Fall '08 term at University of Texas at Austin.

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