MAT 521Spring Lecture 4

# MAT 521Spring Lecture 4 - Lecture 4 Section 1.8...

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Lecture 4 Section 1.8: Combinations II Example 1.8.5 Playing Cards. A deck of 52 cards containing 4 aces is shuffled thoroughly and the cards are distributed among 4 players so that each player receives 13 cards. We shall determine the probability that each player will receive one ace. Method 1: p 1 = the probability that the 1 st player receives one ace = 1 4 12 48 / 13 52 ; p 2 = the probability that the 2 nd player receives one ace from the remaining deck = 1 3 12 36 / 13 39 ;

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p 3 = the probability that the 3 rd player receives one ace from the remaining deck = 1 2 12 24 / 13 26 ; p 4 = the probability that the 2nd player receives one ace from the remaining deck = 1 1 12 12 / 13 13 . p = p 1 p 2 p 3 p 4 = [(13) 4 (4!)(48!)]/52! Method 2 (book’s method) :
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MAT 521Spring Lecture 4 - Lecture 4 Section 1.8...

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