2. (20 points) Find the number of different four-digit numbers that can be obtained by rearranging the digits of the number 2021 (including this number itself).
Answer: 9.

Solution: The number of options can be found by enumerating the permutations of the digits: 2021, 2012, 2201, 2210, 2102, 2120, 1022, 1202, 1220.

The number of options can also be calculated using combinatorial methods. The position of zero can be chosen in three ways, as it should not be the first. Then, in three ways, we choose the position of 1, and on the two remaining places, we put the twos. In the end, we get $3 \cdot 3=9$ possible numbers.