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Disc-a5 - 4 ~ 4 ± K ± K 5 | How many such poker hands are...

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1. How many ways can you arrange the seven characters a , b , c , d , 1 , 2 , 3 in a row so that (a) the letters are in alphabetical order ? You can place the numbers anywhere in the seven positions of the row, so there are 7 6 5 = 210 ways to place the numbers. As the letters must be in alphabetical order, the numbers determine the 210 ways. (b) the letters are in alphabetical order and the numbers are in increasing order ? We just have to decide which of the 7 positions will contain numbers and which will contain letters. So the answer is 7 3 ± = 7 4 ± = 7 6 5 3 2 1 = 35 (c) no two letters are next to each other ? The pattern of letters and numbers must be LNLNLNL. There are 4! to put letters in the positions marked L and 3! ways to put numbers in the positions marked N. So the answer is 4!3! = 24 6 = 144 . 2. A poker hand is called two pairs if it contains two cards of one value, two cards of another value, and one card of unmatched value. For example
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Unformatted text preview: , 4 ~ 4 ± K ± K } 5 | . How many such poker hands are there ? You can pick the two matched values in & 13 2 ± = 78 ways. There are & 4 2 ± = 6 ways to choose two cards from the four cards of a given value. The un-matched card can be any of the 44 cards whose values are di/erent from the two chosen matched values. So the answer is 78 & 6 & 6 & 44 = 123 ; 552 3. Six people join hands for a circle dance. In how many ways can they do this? Now write down all the ways that three people can join hands for a circle dance . You can arrange six people in a line in 6! = 720 ways, so you can arrange them in a circle in 720 = 6 = 120 ways. Call the people in the second part A , B , and C . Then the arrangements are A B C and A C B so there are 3! = 3 = 2 of them....
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This note was uploaded on 07/13/2011 for the course MAD 2104 taught by Professor Staff during the Spring '08 term at FAU.

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