Lecture 3 - Probability and Statistics in the Life Sciences...

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Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 3 (chap3) Donghyung Lee
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Section 3.8 Counting (supplement) X-factorial The factorial of a non-negative integer x, denoted by x!, is the product of all positive integers less than or equal to x. Ex1) 5!=? Ex2) 3!/5!=? ! ( 1)( 2) (2)(1) 1! 1 0! 1 x x x x = - - = =
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Section 3.8 Counting (supplement) Permutations An ordered collection of distinct elements. The number of r -permutations (each of size r ) from a set S with n elements (size n ) is denoted by When counting groups of times (where the order inside the group changes the group), we use a permutation. ! , ( )! n r n P n r n r = -
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Section 3.8 Counting (supplement) Example How many different ordered arrangements of 2 could be selected from the 3 items A , B , and C ? AB , BA , AC , CA , BC , and CB 6 ordered arrangements are possible! Each arrangement is known as a permutation . 3 2 3! 3 2 1 6 6 (3 2)! 1! 1 P = = = = -
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Counting (supplement) Combinations An unordered collection of distinct elements. The number of r -combinations (each of size r ) from a set S with n elements (size n ) is denoted by When counting groups of times (where the order inside the group does not change the group), we use a combination. ! , !( )! n
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Lecture 3 - Probability and Statistics in the Life Sciences...

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