Answer
2520 strings
Work Step by Step
Total Number of arrangements of n objects if all are different = n!
If r! of them are same number of ways are given by $\frac{n!}{r!}$
because if the element that is repeated is exchanged with the similar element at some other position, it does not create a new outcome.
In our case we have two $0s$, three $1s$, five $2s$ and the string length is 10
So $\frac{10!}{2!.3!.5!}$ = 2520 strings
