Cardinality of Set of Subsets/Also presented as

Theorem
This result is also presented in the form:


 * The number of combinations of $n$ objects taken $m$ at a time

or:
 * The number of selections of $n$ objects taken $r$ at a time

or:
 * The number of ways of selecting $m$ objects out of $n$

or:
 * The number of ways of choosing $m$ objects from $n$ where order does not matter

or:
 * The number of ways of choosing a set of $m$ elements from the $n$ elements of the set $S$

Such wording is insufficiently precise for.