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Subsets with a fixed element
A portfolio universe has instruments. How many subsets (the empty subset is allowed) contain one particular instrument?
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Hint
Once the special instrument is forced in, decide about each of the others independently.
Solution
- The particular instrument must be in the subset, so its status is fixed.
- Each of the other instruments is either in or out, giving choices each.
- The total is .
- Therefore the number of subsets is .
Answer: