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

MathyGoo13 Mar 13, 2022

#1**+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.

BuilderBoi Mar 13, 2022

#2**+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 ₯.

BuilderBoi Mar 13, 2022

#3**+2 **

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

Total subsets possible = 2^{5} = 32

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

ElectricPavlov
Mar 13, 2022