Question
The number of different 6-digit numbers that can be formed using the three digits 0, 1 and 2 is
A.
$${3^6}$$
B.
$$2 \times {3^5}$$
C.
$${3^5}$$
D.
None of these
Answer :
$$2 \times {3^5}$$
Solution :
Ways : \[\begin{array}{*{20}{c}}
\times \\
2
\end{array}\,\,\begin{array}{*{20}{c}}
\times \\
3
\end{array}\,\,\begin{array}{*{20}{c}}
\times \\
3
\end{array}\,\,\begin{array}{*{20}{c}}
\times \\
3
\end{array}\,\,\begin{array}{*{20}{c}}
\times \\
3
\end{array}\,\,\begin{array}{*{20}{c}}
\times \\
3
\end{array}\]
0 cannot go in the units place.
∴ the required number of numbers \[ = 2 \times {3^5}.\]