The number of integers greater than 3000 that can be formed by any number of digits from 0,1,2,3,4,5 without repetition in each number is 
 

$4 digit numbers begin with 3,4,5=3\left({ }^5{P}_3\right)=180$

$5 \mathrm{digit} \mathrm{numbers} \mathrm{formed} \mathrm{using} 0,1,2,3,4,5{=}^6{\mathrm{P}}_5-{ }^5{\mathrm{P}}_4=600$

$6 \mathrm{digit} \mathrm{numbers} \mathrm{formed} \mathrm{using} 0,1,2,3,4,5=6!-5!=600$

$$\begin{gathered} \mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{numbers} \mathrm{greater} \mathrm{than} 3000 \\ \mathrm{using} 0,1,2,3,4,5=1380 \end{gathered}$$