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How many subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} contain the number 5 and have 3 elements?

 May 31, 2021
 #1
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There are 27 subsets.

 May 31, 2021
 #2
avatar+119776 
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Since  5   is already member  of the set.....we  just  want to choose  any 2  of  the remaining 9 elements for the other two members  of  the set.....

 

So

 

C( 9,2)   =   36    subsets

 

 

cool cool cool

 May 31, 2021
 #3
avatar+32612 
+2

10 c 3 = 120 subsets with 3 elements

   each element has a   3 out of 10 chance of being in teh subset    3/10 * 120 = 36   substes with the number '5'

 May 31, 2021

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