Lecture11[1]

Lecture11[1] - Lecture 11 Combinations Section 4.1 STAT...

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Combinations Section 4.1 1 STAT 225, Dallas Bateman, Spring 2010 Lecture 11
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Combinations 2 STAT 225, Dallas Bateman, Spring 2010
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Combinations In some problems (e.g. dealing cards) we do not care about the order that the objects are in. In this case, we deal with combinations rather than permutations: If order matters Permutations If order does not matter Combinations Since order doesn’t matter, then we are counting some objects multiple times: 3 STAT 225, Dallas Bateman, Spring 2010
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Combinations Here we take into account the fact that we are counting r multiple times 4 STAT 225, Dallas Bateman, Spring 2010
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Using a Calculator There should be a button on most calculators to perform permutations. There should also be a button allowing you to perform combinations. If there is not, all calculators should have a factorial button (!) which allows you to compute using the formula. r n C r n P 5 STAT 225, Dallas Bateman, Spring 2010
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Combinations: Example #1 A child has 5 different toys in his toy box. He is only allowed to take two of his toys with him on a family outing. How many different sets of toys can he take? Suppose his toys are T1 , T2 , T3 , T4 , T5 Remember: order does NOT matter Therefore, choosing ( T1 & T2 ) is the same as choosing ( T2 & T1 ) 6 STAT 225, Dallas Bateman, Spring 2010
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Combinations: Example #1 Since there are few enough possibilities, let’s list them just for fun: T1, T2 T2, T3 T3, T4 T4, T5 T1, T3 T2, T4 T3, T5 T1, T4 T2, T5 T1, T5 10 12 120 ! 3 ! 2 ! 5 )! 2 5 ( ! 2 ! 5 2 5 C Notice, for example, that T1,T2 is counted, but T2,T1 is not counted. This is because the order does not matter; therefore, they are treated as the same event.
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Lecture11[1] - Lecture 11 Combinations Section 4.1 STAT...

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