SOLUTION: How many even numbers less than 500 can be formed from the integers 1,2,3,4,5 with each integer being used at most once?

1-digit numbers:
There are exactly 2 even 1-digit numbers, 2 and 4

2-digit numbers:
We can choose the second digit 2 ways, either 2 or 4.
For each of those ways to choose the second digit, we 
can choose the first digit any of the remaining 4 ways.

That's exactly 2*4 = 8 two-digit numbers
[We could just list them {12,14,24,32,34,42,52,54}]

3-digit numbers:
We can choose the 3rd digit 2 ways, as 2 or 4.
For each of those 2 ways to choose the 3rd digit, we can
choose the first digit 3 ways.  
[If we choose the 3rd digit 2, we can choose the first digit as
1,3, or 4, and if we choose the 3rd digit 4, we can choose the
1st digit 1,2, or 3]
For each of those choices for the 3rd and 1st digits, we can choose
the middle digit any of the remaining 3 ways.

So the number of 3-digit numbers is 2*3*3 = 18 ways. 

Answer: 2+8+18 = 28 even numbers less than 500 that 
can be formed from the integers 1,2,3,4,5 with each 
integer being used at most once.

Edwin