How to calculate: (Number of sets in power set size n) - (Number of sets in power set size n that have less than or equal to m items) I know that power set size is 2^n, but how may one find the size 2^n - f(m), where f(m) is the size of all sets less than or equal to m (in powerset 2^n).

Example:

when n = 4, m = 2; size = 5

{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}

* Deleted: {},{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d}*

Any suggestions on how to do this? I am aware than as n gets larger, m will become less and less significant compared to the size of the powerset.
Hint:  how many subsets are there of size $0$? Of size $1$? Of size $k$?  Now the number removed is the sum from $0$ to $m$ of the number of subsets.
There is an explicit formula: the number of subsets of $\{1,\ldots,n\}$ of size more than $m$ is
$$
\sum_{k=m+1}^n \binom{n}{k}.
$$