How many even numbers less than $500$ can be formed using the digits $1$, $2$, $3$, $4$ and $5$?
Each digit may be used only once in any number.
I first tried by using the formula for permutations:
$$ 3P1 \times 6 = 18 $$
But the answer is $28$.
So I tried again, this time by listing all of the possible permutations:
- $132$
- $142$
- $152$
- $124$
- $134$
- $154$
- $214$
- $234$
- $254$
- $312$
- $342$
- $352$
- $314$
- $324$
- $354$
- $412$
- $432$
- $452$
I still get $18$.
What am I doing wrong?