How many numbers greater than $4000$ can be formed using $0,2,4,5,7$? 
How many four digit or five digit numbers greater than $4000$ can be formed using $0,2,4,5,7$, if none of the digits are repeated and the numbers formed are even?

I've tried all the ways I can think of to do this question but I always get a different answer to the answer sheet (the correct answer is 108 according to the book). I'm not really sure how to guarantee that it ends in an even number. Any help would be greatly appreciated!

The strategy should be taking care of the first and last digits, then permutate the rest of the numbers for the middle digits. To end with an even number, you can only use 0,2,4 for the last digits. You can not use 0 as the first digit.
Choosing from 0,2,4,5,7

*

*For 5 digits even number
a. First digit even (2 choices), last digit even (2 choices), the rest 3 permutate for the middle 3 digits (3x2 choices)
$\to$ 2x2x3x2=24
b. First digit odd (2 choices) , last digit even  (3 choices ), the rest 3 permutate for the middle 3 digits(3x2 choices)
$\to$ 2x3x3x2= 36


*For 4 digits even number greater than 4000
a. First digit odd (2 choices ), last digit even (3 choices ), the rest 3 permutate for the middle 2 digits (3x2 choices)
$\to$ 2x3x3x2=36
b. First digit even (1 choice), last digit even (2 choices), the rest 3 permutate to for the middle 2 digits (3x2 choices)
$\to$ 1x2x3x2=12
Total:  24+36+36+12=108
