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Q)

The no. of ways in which any four letters can be selected from the word 'ENTREE' is

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

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A)
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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