SOLUTION: Hello, I am very stuck on this problem, so if you could provide a very in-depth explanation with step-by-step instructions on how to solve it, that would be greatly appreciated, th

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Question 1183404: Hello, I am very stuck on this problem, so if you could provide a very in-depth explanation with step-by-step instructions on how to solve it, that would be greatly appreciated, thank you so much!:
Camy made a list of every possible distinct five-digit positive even integer that can be formed using each of the digits 1,3,4,5, and 9 exactly once in each integer. What is the sum of the integers on Camy's list?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Since this time Camy wants five-digit even integer, which means that the number "4" has to be at the unit digit and only 1, 3, 5, 9+ can be moved freely.

There will be 4%21+=+24 times the even number 4 will be used (arrangements), so
4+%2A+24+=+96
As for the remaining 4 numbers, their average (or mean) is %281%2B3%2B5%2B9%29%2F4=4.5
then, the sum of the integers on Camy's list is:

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by the other tutor is fine. Here is a different approach.

Since 4 is the only even digit of the five given digits, the number of numbers in the list will be the number of ways the other four digits can be ordered, which is 4!=24.

So every digit in the units column will be 4; the sum of those digits is 24*4=96.

In each of the other columns, each of the other four digits occurs 6 times. The sum of the other four digits is 18. So the sum of the digits in each column except the units column is 6*18=108.

The sum of all the numbers in the list is then

108(10000+1000+100+10)+96 = 1111976