The total number of numbers from 1000 to 9999 (both inclusive) that do not have four different digits is 
 

$$\begin{gathered} \mathrm{Number} \mathrm{of} 4 \mathrm{digit} \mathrm{numbers} \mathrm{with} \mathrm{distinct} \mathrm{digits}=9\left({ }^9{\mathrm{P}}_3\right)=9\times 9\times 8\times 7 \\ =4536 \end{gathered}$$$\mathrm{Number} \mathrm{of} \mathrm{numbers} \mathrm{from} 1000 \mathrm{to} 9999=9999-1000+1=9000$

The total number of numbers from 1000 to 9999 (both inclusive) that do not have four different digits =9000-4536=4464