$\begin{array}{1 1} 15 \\ 11 \\ 9 \\ 7 \end{array} $

There are 3 cases.

Case (i)

4 selected alphabets includes 3 $E^s$

and one letter from N,T,R is selected in $^3C_1=3$ ways.

Case (ii)

4 selected alphabets includes 2 $E^s$

and two alphabets are selected from N,T,R in $^3C_2=3$ ways.

Case (iii)

4 selected alphabets includes 1 $E$

and the remaining three alphabets are N,T,R. (selected in 1 way)

$\therefore$ The required no. of selection$= 3+3+1=7$

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