Question 481431: How many even 4-digit numbers can be made using 0, 2, 3, 5, 6, 9 if no repeats are allowed?
Answer by kingme18(98)   (Show Source):
You can put this solution on YOUR website! Recall that an even number ENDS with an even digit:
(digit) (digit) (digit) (even)
That means that the only digits this 4-digit number could end in are 0, 2, or 6, so there are 3 options for the last digit:
(digit) (digit) (digit) (3 options)
Once you have the last digit, you can work backwards. You started with 6 digits, and you've used one digit. I don't know what one it was, but it doesn't matter: you used one, so you have 5 left to choose from: there are 5 options for the next digit.
(digit) (digit) (5 options) (3 options)
Now you've used 2 digits, so there are 4 options for the next one. Once you've used that, you're down to 3 options for the first digit.
(3 options) (4 options) (5 options) (3 options)
To find out how many numbers you could make, you simply multiply: 
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