Unusual dice

Roll simultaneously a hundred 100-sided dice, and add the resulting values. The set of possible outcomes is, of course, $\{100, 101, \dotsc, 10000\}.$ Note that there is only one way to obtain the outcome 100—all dice showing a 1. There is also only one way to obtain the outcome 10000—all dice showing 100. For the outcome 101, there are exactly 100 different ways to obtain it: all dice except one show a 1, and one die shows a 2. The follow-up question is: