1.57 In a shooting competition, there are 8 clay targets hanging in 3 columns as shown in the right figure. A marksman will shoot down all the targets according to the following rules:
(1) First, choose a column where a target will be shot down;
(2) Then, in the selected column, shoot down the lowest remaining target.
How many different sequences are there to shoot down these 8 targets?
[Solution 1] First, consider the leftmost column. The number of possible orders to hit these 3 targets is $C_{8}^{3}$. Next, consider the middle column. The number of different orders to hit these 2 targets is $C_{5}^{2}$. The remaining 3 numbers represent the order to hit the last column of 3 targets. Therefore, the total number of different orders is
$$
S=C_{8}^{3} \cdot C_{5}^{2}=56 \times 10=560 .
$$
[Solution 2] The total number of permutations of the 8 target numbers is $8!$. However, the order in which the targets in each column are hit must be from bottom to top, and cannot be arranged arbitrarily. Therefore, the total number of different orders is
$$
S=\frac{8!}{3!2!3!}=\frac{8 \times 7 \times 6 \times 5 \times 4}{2 \times 6}=560 .
$$