Example 1: From the 10 numbers $0,1,2,3,4,5,6,7,8,9$, select 3 numbers such that their sum is an even number not less than 10. The number of different ways to do this is $\qquad$
Solution: To select 3 numbers from 10 numbers such that their sum is even, the 3 numbers must all be even or 1 even and 2 odd.
When all 3 numbers are even, there are $\mathrm{C}_{5}^{3}$ ways to choose;
When there is 1 even and 2 odd numbers, there are $\mathrm{C}_{5}^{1} \mathrm{C}_{5}^{2}$ ways to choose. Since their sum is an even number not less than 10, we list the sums that are even and less than 10, which are as follows:
$$
\begin{array}{l}
(0,1,3),(0,1,5),(0,1,7), \\
(0,3,5),(0,2,4),(0,2,6), \\
(1,2,3),(1,2,5),(1,3,4) .
\end{array}
$$

Therefore, the number of ways that meet the requirements of the problem is
$$
C_{5}^{3}+C_{5}^{1} C_{5}^{2}-9=51 \text { (ways) . }
$$