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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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- Spring '08