<s>[INST] How many different 4 letter words can be selected from the word ADVANCED? 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 ?
 [/INST] $606$ is correct.
A g.f. way is to find the coefficient of $x^4$ in $4!(1+x)^4(1+x+\frac{x^2}{2!})^2$
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