2. How many four-digit numbers can be formed, the sum of whose digits is 3? List these numbers.
2. For writing numbers, we use digits

$0,1,2,3,4,5,6,7,8,9$

Since the sum of the digits is three, we can exclude all digits starting from four.

$0,1,2,3,4,5,6,7,8,9$

A number cannot start with zero, so the first digit can be one of the three digits $1,2,3$. The further solution will be represented in the form of a diagram:

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-030.jpg?height=229&width=871&top_left_y=1002&top_left_x=615)

Now we need to choose the second digit for each of the three cases.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-030.jpg?height=340&width=857&top_left_y=1395&top_left_x=614)

Similarly, we will determine the third and fourth digits.

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-030.jpg?height=520&width=1196&top_left_y=1850&top_left_x=447)

The obtained numbers are:

| $1002 ;$ | $1101 ;$ | $2001 ;$ | $3000 ;$ |
| :--- | :--- | :--- | :--- |
| $1011 ;$ | $1110 ;$ | $2010 ;$ |  |
| $1020 ;$ | $1200 ;$ | 2100. |  |

Answer: 10 numbers.