Question 1128074: How many three-digit numbers may be formed using elements from the set {1,2,3,4,5,67,8,9} if no element may be used more than once in a number and the number must be even?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You are using the digits 1 through 9 (no zero),
so there are  digits to choose from.
An even number must end in 0, 2, 4, 6, or 8.
Your even three-digit numbers must end in 2, 4, 6, or 8.
That gives you  choices for the last digit.
For each choice, you have  unused digits to use as second (tens) digit,
to get  two-digit ending sequences.
Each of those two-digit ending sequence choices
leaves you  unused digits you can choose as the first (hundreds) digit,
for a total of 
three-digit even numbers with no repeated digits.
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