A 
-subset is a subset
of a set on 
elements containing exactly 
elements. The number of 
-subsets on 
elements is therefore given by the binomial
coefficient 
.
For example, there are 
2-subsets of 
,
namely 
, 
, and 
.
The 
-subsets of a list
can be enumerated in the Wolfram Language
as Subsets[list,
k
].
Summing the numbers of distinct 
-subsets on a set of 
elements over all sizes 
, 1, ..., 
gives the total number of subsets,
 |
-Subsets." §1.5.5 in