Question

All possible four digit numbers are formed using the digits $0,1,2,3$, so that no number has repeated digits. The number of even numbers among them is?

• A. $9$
• B. $18$
• C. $10$
• D. None of these

Answer 1

The correct option is B

$18$

Explanation for the correct option:

Finding the number of possibility.

The digits are $0,1,2,3$

There are four positions in which digits can be arranged.

In first position, zero cannot be placed. Since four digit number cannot be formed with zero. So, we can form digits with $1,2,3$. Thus there are $3$ possibilities.

In second position, we can place any of the remaining three digits. So it has $3$ possibilities.

In third position, we can place the remaining two digits. So it has $2$ possibilities.

In fourth position, we can place either $0or2$, because the number should be an even number. So, it has only $1$ possibility.

Thus, to form an even four digit number, the number of possibilities is

$$\begin{gathered} =3\times 3\times 2\times 1 \\ =18 \end{gathered}$$

Hence, option (B) $\mathbf{18}$ is the correct answer.