Example 1. From the numbers $1,2, \cdots, 14$, select $a_{1}, a_{2}, a_{3}$ in ascending order, and $a_{2}-a_{1} \geqslant 3, a_{3}-a_{2} \geqslant 3$. How many different ways of selection are there that meet the conditions? (1989, National High School Competition)
Destruct the following model:
Take 10 identical white balls and arrange them in a row, take 5 identical black balls and divide them into 3 groups in the order of $2,2,1$, then insert them into the 10 gaps between the white balls, from left to right, excluding the left end but including the right end. There are $C_{10}^{3}$ ways to insert. Each insertion method corresponds to an unordered set. As shown in the figure: $\square$

etc. Therefore, the number of different ways to draw is $C_{10}^{3}=120$.

