13. Place 1996 indistinguishable balls into 10 different boxes, such that the $i$-th box contains at least $i$ balls $(i=1,2, \cdots, 10)$. How many different ways are there to do this?
13. First, place $i$ balls in the $i$-th box $(i=1,2, \cdots, 10)$, i.e., place 1 ball in the 1st box, 2 balls in the 2nd box, $\cdots$, up to 10 balls in the 10th box. This results in a total of $1+2+3+\cdots+10=55$ balls. There are still $1996-55=1941$ balls left. Thus, the problem is reduced to placing 1941 balls into 10 boxes (allowing some boxes to remain empty). There are $C_{1950}^{9}$ ways to do this.