All possible four digit numbers are formed using the digits 0, 1,…

MCQ

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
$18$
✓
$10$
D
None of these

✓

Answer

Correct option: C.

$10$

c
(c) In forming even numbers, the position on the right can be filled either $0$ or $2$. When $0$ is filled, the remaining positions can be filled in $3\;!$ ways and when $2$ is filled, the position on the left can be filled in $2$ ways ($0$ cannot be used) and the middle two positions in $2\;!$ ways ($0$ can be used). Therefore the number of even numbers formed $ = 3\;! + 2(2\;!) = 10$.

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