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Sum of All 4-Digit Numbers with Digits 2, 4, 6, 8
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- To find the sum of all 4-digit numbers containing the digits 2, 4, 6, and 8 without repetition, we need to consider all possible permutations of these digits.
- There are a total of 4! (4 factorial) permutations of these digits, which is equal to 24.
- Each digit appears in the units, tens, hundreds, and thousands place in 6 permutations each.
- Therefore, the sum of all 4-digit numbers formed by these digits can be calculated by finding the sum of each digit multiplied by its place value in the number.
- The sum of the digits 2, 4, 6, and 8 is 20.
- To calculate the total sum, we multiply 20 by 24 (the total number of permutations).
- Therefore, the sum of all 4-digit numbers containing the digits 2, 4, 6, and 8 without repetition is 20 x 24 = 480.

Explanation:
- The key to solving this problem lies in understanding the permutations of the given digits and how they contribute to the overall sum.
- By considering all possible arrangements of the digits and calculating the sum for each arrangement, we can find the total sum of all 4-digit numbers that can be formed using the digits 2, 4, 6, and 8.
- This method ensures that we account for all possible combinations without repetition and arrive at the correct answer.