Can someone explain why the total number of ways of selecting one or more of n different things is $2^n -1$ and that of selecting zero or more things out of $p$ identical things is $p+1$. I am confused in this alot plzz help.
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Distinct: There are $n$ objects. Each is either chosen are not, two choices. This makes $2\cdot2\cdot2\cdots2=2^n$. However, the question specified "one or more", so you need to subtract out the case where you nothing is chosen, so $2^n-1$.
Indistinguishable: All that matters is the number of objects you chose, which can be anywhere between $0$ and $p$. There are $p+1$ numbers in this range.
Mike Earnest
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