Question:
How many number of four digits can be formed with the digits 1, 3, 3, 0?
Solution:
The given digits are 1, 3, 3, 0.
Total numbers that can be formed with these digits $=\frac{4 !}{2 !}$
Now, these numbers also include the numbers in which the thousand's place is 0.
But, to form a four digit number, this is not possible.
$\therefore$ Numbers in which the thousand's place is fixed as zero $=$ Ways of arranging the remaining digits $(1,3$ and 3$)$ in three places $=\frac{3 !}{2 !}$
$\therefore$ Four digit numbers $=$ Total numbers $-$ Numbers in which the thousand's place is 0
$=\frac{4 !}{2 !}-\frac{3 !}{2 !}=9$