How many even $4$-digit numbers can be made such that the sum of ones and tens $=4$??

Question

We have the set of numbers $(0,1,...,9)$.

I try solving this and I get result $=270$.

$$\frac{9!}{8!}*\frac{10!}{9!}*3=270$$

I used the formula for variations: $\frac{n!}{(n-k)!}$

Is this correct and is there another way of solving this?