Question
The total number of ways in which a beggar can be given at least one rupee from four 25-paisa coins, three 50-paisa coins and 2 one-rupee coins, is
A.
54
B.
53
C.
51
D.
None of these
Answer :
54
Solution :
\[\begin{gathered}
\underline {\begin{array}{*{20}{c}}
{Possibilities}&{Selection} \\
\begin{gathered}
{\text{At least one rupee coin, any number of 50 - paisa coins,}} \hfill \\
{\text{ any number of 25 - paisa coins}} \hfill \\
\end{gathered} &{2 \times 4 \times 5} \\
{{\text{At least two 50 - paisa coins, any number of 25 - paisa coins}}}&{2 \times 5} \\
{{\text{One 50 - paisa coin, at least two 25 - paisa coins}}}&{1 \times 3} \\
{{\text{Four 25 - paisa coins}}}&1
\end{array}} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\therefore \,\,{\text{the required number of ways}} = {\text{54}} \hfill \\
\end{gathered} \]