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Ten people, including Fred, are in the Jazz Club. They decide to form a 3-person steering committee. How many possible committees can be formed that do not include Fred? Do you notice a relationship between your answers of the three parts of this problem?

 Mar 20, 2015

Best Answer 

 #1
avatar+130477 
+12

Using my two previous answers.....

Total committees - Total committtees that include Fred = Total committees that don't include Fred

So we have

120 - 36  =  84 committees that don't include Fred

Note this is the same as C(9,3) = choosing  any 3 of 9 people that don't include Fred

 

  

 Mar 20, 2015
 #1
avatar+130477 
+12
Best Answer

Using my two previous answers.....

Total committees - Total committtees that include Fred = Total committees that don't include Fred

So we have

120 - 36  =  84 committees that don't include Fred

Note this is the same as C(9,3) = choosing  any 3 of 9 people that don't include Fred

 

  

CPhill Mar 20, 2015
 #2
avatar+118703 
+4

total number of commities - no restrictions         (10!3!×(103)!)=120

 

total number that Fred is in         (9!2!×(92)!)=36

 

 

total number that Fred is not ine       (9!3!×(93)!)=84

 

84+36=120

These 2 are complementary events,

either one happens OR the other happens. 

 Mar 21, 2015

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