combinatorics problem involving even numbers?
The problem is: How many even numbers greater than 40,000 may be formed using the digits 3, 4, 5, 6 and 9 if each digit must be used exactly once in each number?
Like all combinatorics problems, I create five spots. The last spot must be used up by 4 or 6, b/c it's even, so we have
_ _ _ _ 2
But then my book says to assign the first spot to 3, because there are 3 numbers left over after choosing two for the last spot. But since I only used one number for the last spot--either 4 or 6---shouldn't the first spot be assigned to 4, and then, accordingly:
4 3 2 1 3 ?