+218 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
+2668 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.
+2668 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 ₯.
+37153 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
