Hint: It is the number of positive solutions of $x_1+x_2+ x_3+x_4 +x_5=100$.
For in how many ways can I distribute candies among $4$ kids, each kid getting one candy at least, and with $\lt 100$ candies distributed?
Imagine I have $100$ candies. I call myself the fifth kid, and if $k$ candies are distributed among the real four, I get the remaining $100-k$. This gives a natural one to one correspondence between distribution of $\lt 100$ candies among $4$ kids, one at least to each, and distributions of $100$ candies among $5$ kids, at least one to each.
Mild modification of the idea takes care of the situation in which we do not have the condition "at least one to each."