Question
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
A.
72
B.
120
C.
14
D.
None of these
Answer :
72
Solution :
\[\begin{gathered}
\begin{array}{*{20}{c}}
{Possibilities}&{Selections}&{Arrangements} \\
{{\text{One pair, one different}}}&{^1{C_1} \times {\,^4}{C_1}}&{^1{C_1} \times {\,^4}{C_1} \times \frac{{3!}}{{2!}} = 12} \\
{{\text{Three different}}}&{^5{C_3}}&{\underline {^5{C_3} \times \,3! = 60} }
\end{array} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\therefore \,\,{\text{the required number of ways}} = 72. \hfill \\
\end{gathered} \]