Given a set $A$, such that $A = \{1,2,\dots,10\}$, is there a formula you can use to quickly determine the number of doubletons that can be produced from the set $A$?
A doubleton for these purposes is defined as a subset of $A$ that contains two elements such as $\{1,2\}$ and $\{3,4\}$.
I know that you can use $2^{\lvert A\rvert}$, where $\lvert A\rvert$ represents the cardinality of set $A$, to determine the number of elements in the powerset of $A$. Is there something similar to find the number of doubletons? Thanks!
The number of doubletons in a set with ten elements is given by $\binom{10}{2}$. This in fact corresponds to the number of non-ordered pairs of elements chosen from ten. In general, if you want the number of sets with $k$ elements chosen from $n$, the answer is $\binom{n}{k}$.