1. Correct Answer: a: 7998
 2. Explanation:
 To solve this problem, we need to find the sum of all 4-digit numbers less than 2000 that can be formed using the digits 1, 2, 3, and 4, without repeating any digit.
 Step 1: Determine the possible numbers
 Since the numbers must be less than 2000, the thousands digit can only be 1. Therefore, the numbers are of the form 1XYZ, where X, Y, and Z are chosen from the remaining digits 2, 3, and 4.
 Step 2: Calculate the number of permutations
 The remaining digits (2, 3, and 4) can be arranged in 3! (3 factorial) ways. This is calculated as:
 \[ 3! = 3 \times 2 \times 1 = 6 \]
 So, there are 6 possible numbers: 1234, 1243, 1324, 1342, 1423, and 1432.
 Step 3: Calculate the sum of these numbers
 Now, we calculate the sum of these numbers:
      ○ 1234
      ○ 1243
      ○ 1324
      ○ 1342
      ○ 1423
      ○ 1432
 Add these numbers together:
 \[ 1234 + 1243 + 1324 + 1342 + 1423 + 1432 = 7998 \]
 Thus, the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3, and 4, where none of the digits is repeated, is 7998.