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How many subsets of the set {1,2,3,4,5} contain the number 5?

 Aug 31, 2018
 #1
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The first is the improper subset {1,2,3, 4, 5}

 

Next...we can choose any 3 of the 4 remaining elements to  include in a set with 5  = 4C3  = 4 more subsets

 

Then, we can choose any 2 of the remaining elements to include in a set with 5  = 4C2  = 6  additional subsets

 

Then, we can choose any 1 of the remaining elements to include in a set with 5  = 4 C1   = 4 additional subsets

 

Lastly...we can  just have a set only including 5   =  1  additional subset

 

Note....these  are just  the sum of the entries in Row 4 of Pascal's Triangle  = 1 4 6 4 1  =  2^4  =  16  subsets  [if we include the improper subset ] 

 

 

cool cool cool

 Aug 31, 2018
edited by CPhill  Aug 31, 2018
edited by CPhill  Aug 31, 2018

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