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# Wierd Question on Subets

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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
+2666
+1

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
+2666
+1

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
+36721
+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
+1

Thank you guys!!

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

Mar 14, 2022