Example 25 A middle school is preparing to form an 18-person soccer team, consisting of students from 10 classes in the first year of high school, with at least one student from each class. The number of allocation schemes is $\qquad$ kinds.
Solve: Fill in 24310. Reason: Construct a partition model, take 18 identical balls and arrange them in a row, use 9 partitions to divide the 18 balls into 10 intervals, the number of balls in the $i$-th interval $(1 \leqslant i \leqslant 10)$ corresponds to the number of student quotas for the $i$-th class. Therefore, the number of quota allocation schemes is equal to the number of ways to insert the partitions. Since the number of ways to insert partitions is $C_{17}^{9}$, the total number of quota allocation schemes is $C_{17}^{9}=24310$.