[EM] Completion methods for Smith Sets

[LAYTON Craig]

>The problem is that step C requires examining every ballot at least 
>once.  If this is a public election, that could require examining and 
>recounting possibly millions of ballots.  With large numbers of candidates,

>the number of possible rankings grows hyper-exponentially, and even 13 
>candidates under consideration would yield more possible rankings than the 
>population of the Earth.  There is no way to represent ranking data in the 
>aggregate; re-examining the entire collection of ballots is the only way to
go.

What is the formula for the number of possible ballots (assuming equal
rankings are possible, as long as at least one rank distinction is made)?

Craig