1. (10 points) A four-digit number, with all digits being distinct, the sum of all digits equals 6, and the number is a multiple of 11. How many such four-digit numbers are there?
A. 6
B. 7
C. 8
D. 9
【Analysis】Given this four-digit number, all digits are different, and the sum of all digits equals 6. Therefore, the four digits that make up the four-digit number are $0, 1, 2, 3$. This number is a multiple of 11, so the sum of the digits in the odd positions equals the sum of the digits in the even positions, which is 3. According to this, we can find the four-digit number that meets the conditions.

【Solution】Solution: According to the problem, the four digits that make up the four-digit number are $0, 1, 2, 3$. Since this number is a multiple of 11, the sum of the digits in the odd positions equals the sum of the digits in the even positions, which is 3. The four-digit numbers that meet the conditions are $3102, 3201$, 1320, 1023, 2310, 2013, a total of 6. Therefore, the answer is: A.