The sum of all 4 digit number containing the digits 2,4,6,8 without repetitions is ?

Question

Answer

Sum of all 4 digit numbers containing the digits 2,4,6,8 without repetitions

To find the sum of all 4 digit numbers containing the digits 2,4,6,8 without repetitions, we need to follow the steps below:

Step 1: Determine the number of possible combinations

Since we have 4 digits to work with, we have 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the fourth digit.

Step 2: Determine the sum of all possible 4 digit numbers

We can find the sum of all possible 4 digit numbers by using the formula for the sum of an arithmetic series: (first term + last term) x (number of terms) / 2.

So, the sum of all possible 4 digit numbers is (2468 + 8642) x 24 / 2 = 555,600.

Step 3: Eliminate the sum of all 3 digit numbers

Since we are only interested in 4 digit numbers, we need to eliminate the sum of all 3 digit numbers that can be formed using the digits 2,4,6,8 without repetitions.

There are 4 choices for the first digit, 3 choices for the second digit, and 2 choices for the third digit.

Therefore, the total number of 3 digit numbers that can be formed is 4 x 3 x 2 = 24.

We can simplify this expression by noticing that each digit appears in each position (units, tens, hundreds) the same number of times (6 times).

So, we can write the expression as (6 x (2+4+6+8) x (1+10+100)) x 24 / 2 = 177,600.

Step 4: Calculate the final answer

To find the sum of all 4 digit numbers containing the digits 2,4,6,8 without repetitions, we simply subtract the sum of all 3 digit numbers from the sum of all possible 4 digit numbers.

Therefore, the sum of all 4 digit numbers containing the digits 2,4,6,8 without repetitions is

Answer

533280