Question

Write all possible $3$-digit numbers (without repeating the digits), by using the digits $9,0,2$.

Answer 1

Step 1: Forming $3$-digit numbers if $0$ is at the hundreds place:

There are two choices:

H	T	O
$0$	$9$	$2$
$0$	$2$	$9$

But the numbers so formed are $2$-digit numbers. So, neglecting this case.

Step 2: Forming $3$-digit numbers if $9$ is at the hundreds place:

There are two choices:

H	T	O
$9$	$0$	$2$
$9$	$2$	$0$

Step 3: Forming $3$-digit numbers if $2$ is at the hundreds place:

There are two choices:

H	T	O
$2$	$9$	$0$
$2$	$0$	$9$

Thus, four $3$-digit numbers (without repeating the digits) can be formed using the digits $9,0,2$ which are as follows:

$902,920,290,209$.