Explain why $2,2-$dimethyl$-3-$ethylpentane is not the correct $IUPAC$ name for $(CH_3)_3C-CH(C_2H_5)_2$?

(N/A) In $IUPAC$ nomenclature,when naming substituted alkanes,substituents must be listed in alphabetical order.
In the name $2,2-$dimethyl$-3-$ethylpentane,the methyl group is listed before the ethyl group,which violates the alphabetical priority rule.
According to $IUPAC$ rules,'ethyl' must precede 'methyl' because '$e$' comes before '$m$' in the alphabet.
Therefore,the correct $IUPAC$ name is $3-$ethyl$-2,2-$dimethylpentane.