How many number of four digits can be formed with the digits 1, 3, 3, 0?
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

$=\frac{4 !}{2 !}-\frac{3 !}{2 !}=9$

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