Question

The number of 5-digits numbers that can be formed using the digits 0, 1, 1, 2, 3 is

Answer 1

$\text{If repetitions are allowed, the no. of 5 digit numbers}$

$\Rightarrow 4\times 5\times 5\times 5\times 5$

4×5×5×5×5=2500

$\text{(since '0' cannot come in first place)}$

$=2500$

$\text{No. of 5 digit numbers in which no number is repeated}$

$\Rightarrow 4\times \frac{4!}{2!}$

$\text{(since '1' occurs twice)}$

$=48$