Question

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

Answer 1

Total number of digits = 4

Total number of 4 digit numbers = $\frac{4!}{2!}$

But, zero cannot be first digit of the four digit numbers.

$\therefore$ Total number of 3 digit numbers = $\frac{3!}{2!}$

$\therefore$ Total number of numbers = $\frac{4!}{2!}-\frac{3!}{2!}$

= $\frac{4\times 3\times 2}{2!}-\frac{(3\times 2!)}{2!}$

= 12-3 = 9

Hence, total number of four digit numbers

= 9.