Task 6.4. On a computer keyboard, the key with the digit 1 is not working. For example, if you try to type the number 1231234, only the number 23234 will be printed.

Sasha tried to type an 8-digit number, but only 202020 was printed. How many 8-digit numbers meet this condition?
Answer: 28.

Solution. It is clear that 2 units were not printed. There are 7 positions where they can be located (they can be in the same position or in different ones):

- X202020;
- 2 X 02020;
- $20 \times 2020$
- $202 \times 020$
- $2020 \times 20$
- $20202 \mathrm{X} 0$
- $202020 \mathrm{X}$.

Case 1. If the first unit is placed in the first position, then there are 7 options left for the second unit (in any of the above positions).

Case 2. If the first unit is placed in the second position, then there are 6 options left for the second unit (in any of the above positions except the first, as this option has already been counted).

Case 3. If the first unit is placed in the third position, then there are 5 options left for the second unit (in any of the above positions except the first and second, as these options have already been counted).

$\cdots$

Case 7. If the first unit is placed in the seventh position, then there is 1 option left for the second unit (only in the seventh position; all other options have already been counted).

In total, there are exactly $1+2+3+4+5+6+7=28$ options.