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Consider the following set of symbols. 

 

\(\{~∑~, ~∯~, ~௹~, ~₯~, ~₿ ~\}\)

 

The number of subsets of this set which contain the ₯ symbol is?

 

a) 32   b) 16    c) 6   d) 2    b) 4

 Mar 13, 2022
 #1
avatar+1382 
+2

I will number these from right to left, starting with 1, going up to 5. The rightmost one is 1, the leftmost is 5. 

 

2 1

2 3

2 4

2 5 

2 1 3 

2 1 4 

2 1 5 

2 3 4 

2 3 5 

2 4 5

2 1 3 4 

2 1 3 5 

2 1 4 5 

2 3 4 5 

2 1 3 4 5 

 

Thus, there is a total of \(\color{brown}\boxed{15}\) subsets with the ₯ symbol. 

 Mar 13, 2022
 #2
avatar+1382 
+2

Here's a better way to get the same answer. 

 

For groups of 2 including  ₯, there is \(4 \choose 1 \) choices, because 1 of them is already taken. 

For groups of 3 including  ₯, there is \(4 \choose 2 \) choices, because 1 of them is already taken. 

For groups of 4 including  ₯, there is \(4 \choose 3\) choices, because 1 of them is already taken. 

For groups of 5 including  \(₯\), there is \(4 \choose 4\) choices, because 1 of them is already taken. 

 

Adding everything up, there is \(\color{brown}\boxed{15}\) subsets that contain ₯.

 Mar 13, 2022
 #3
avatar+36417 
+2

Question BB :    Can a subset have just one element ?       If so, there is one more possibility

 

Total subsets possible =   25  = 32

     I believe 1/2 of these would contain the symbol     = 16 subsets

ElectricPavlov  Mar 13, 2022
 #4
avatar
+1

Thank you guys!!

Yes, subsets of just 1 term are possible. !!

 Mar 14, 2022

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