How many different 4 letter words can be selected from the word ADVANCED?

Question

My attempt : $A-2 , D -2 , V - 1, N -1 , C -1 , E -1 $

$XXXX$ words $=0 $

$XXXY$ words $=0 $

$XXYY$ words $= \binom{2}{2}\times \frac{4!}{2!2!} = 6$

$XXYZ$ words $= \binom{2}{1}\times \binom{5}{2} \times \frac{4!}{2!} =240$

$XYZW$ words $= \binom{6}{4}\times 4!=360$

So the answer is $606$ ?

Is it correct ?

Answer 1

$606$ is correct.

A g.f. way is to find the coefficient of $x^4$ in $4!(1+x)^4(1+x+\frac{x^2}{2!})^2$