8,9,10 |

How many six-digit numbers exist where each subsequent digit is less than the previous one?
The first method. Each such number corresponds uniquely to the selection of six digits from the number 9876543210. The second method. To obtain a number with "decreasing digits," you need to strike out any four digits from the number 9876543210.

## Answer

$$
C_{10}^{6}=C_{10}^{4}=210 \text { numbers. }
$$

Problem