How many $4$ letter words can be formed from the word "CORONAVIRUS". Letters: $C$, $O$ ($2$ times), $R$ ($2$ times), $N$, $A$, $V$, $I$, $U$ and $S$.
The number of $4$ letter words from $C$, $N$, $A$, $V$, $I$, $U$ and $S$ is $7\times 6\times 5\times 4=840$.
The number of $4$ letter words from two $O$ or two $R$ while other $2$ letters are different is $\displaystyle \binom{2}{1}\times \binom{8}{2}\times \frac{4!}{2!}=672$.
The number of $4$ letter words from two $O$ and two $R$ together is $\displaystyle \frac{4!}{2!\times 2!}=6$
Total number of ways should be $840+672+6=1518$.
But this is not the right answer given. What am I doing wrong? What cases I am missing here? Please help!!!
Thanks in advance!!!

You could also use the exponential generating function:
$(1+x+x^2/2)^2(1+x)^7$
The fourth power term is $\dfrac{617x^4}{4}$.  The number of 4 letter words would be the coefficient of $x^4/4!$. So $617 \times 6=3702$.
