If the words formed by using the letters of the word HARFET are arranged in the form of dictionary, then 261th word

Given letters in A.O are $\cancel{\text{A}},\cancel{\text{E}},\cancel{\text{F}},\cancel{\text{H}},\cancel{\text{R}},\cancel{\text{T}}$

Required word with rank 261

$261=120+120+6+6+6+2+1$

$=2\times 5!+3\times 3!+1\times 2!+1$

Words that begin with,

$\begin{array}{c}\begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}A& X\end{array}& X\end{array}& X\end{array}& X\end{array}& X& =& 5!\end{array}\\ \begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}E& X\end{array}& X\end{array}& X\end{array}& X\end{array}& X& =& 5!\end{array}\\ \begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}F& A\end{array}& E\end{array}& X\end{array}& X\end{array}& X& =& 3!\end{array}\\ \begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}F& A\end{array}& H\end{array}& X\end{array}& X\end{array}& X& =& 3!\end{array}\\ \begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}F& A\end{array}& R\end{array}& X\end{array}& X\end{array}& X& =& 3!\end{array}\\ \begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}F& A\end{array}& T\end{array}& E\end{array}& X\end{array}& X& =& 2!\end{array}\\ \begin{array}{cccc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}F& A\end{array}& T\end{array}& H\end{array}& E\end{array}& R& =& 1!\end{array}\end{array}$

                                             $\boxed{261}$

Required word :  FATHER

    (or)

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