Sol. $\quad \mathrm{N} \rightarrow 2, \mathrm{A} \rightarrow 2, \mathrm{I} \rightarrow 2, \mathrm{E}, \mathrm{X}, \mathrm{M}, \mathrm{T}, \mathrm{O} \rightarrow 1$

$\begin{array}{l|c|c|}\hline {\text { Category }} & {\text { Selection }}& {\text { Arrangement }} \\ \hline \text {2 alike of one kind and 2 alike of other kind} & {^{3} \mathrm{C}_{2}=3} & {3 \times \frac{4 !}{2 ! 2 !}=18} \\ \hline \text {2 alike and 2 different} & ^{3} \mathrm{C}_{1} \times{^{7} \mathrm{C}_{2}} & {^{3} \mathrm{C}_{1} \times^{7} \mathrm{C}_{2} \times \frac{4 !}{2 !}=756} \\ \hline \text { All 4 different } & {^{8} \mathrm{C}_{4}} & {^{8} \mathrm{C}_{4} \times 4 !=1680}\end{array}$

Total $=2454$