Lecture11[1]

# Lecture11[1] - Lecture 11 Combinations Section 4.1 STAT 225...

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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
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
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
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 225...

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