SOLUTION: 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?
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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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