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How many subsets of the set  \(\{1,2,3,4, 5, 6, 7, 8, 9, 10\}\) contain the number 5?

 May 6, 2019
 #1
avatar+2856 
+2

There are 2^10 different subsets in the original set.

 

Now let us just subtract subsets without a 5

 

Let us just pretend you have set without a 5

 

So {1 2 3 4 6 7 8 9 10} Is your new set

 

So how many subsets can you make from that?

 

2^9 subsets

 

2^10 - 2^9 = 512 different subsets

 

NOTE: 2^10 - 2^9 is NOT 2.

 

So there you have it! :D:D:D

 May 6, 2019
edited by CalculatorUser  May 6, 2019
 #2
avatar+219 
-3

To solve this problem, do this...

 

There are 10 numbers, so the first term of the expression is 2^10. Then subtract that by 2^9 to find the answer.

 

2^10 = 1024

2^9 = 512

 

1024-512 = 512

 

There are 512 subsets that do not contain the number 5.

 

~~Hypotenuisance

 May 6, 2019

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