Calculate the number of different vote totals, using the plurality voting method (see Example 2.25), when there are \(m\) candidates and \(n\) voters and each voter need not vote.

We will use combinations with replacement here, summing the numbers for \(0\) through to \(n\) votes:

\[\sum_{i=0}^{n} C^{R}(m, i) = \sum_{i=0}^{n} C(m+i-1, i) = \sum_{i=0}^{n} \binom{m+i-1}{i}\]