MathsLinks

I have a ten digit number. The first digit tells me how many zeros are in the number. The second digit tells me how many ones are in the number. The third digit tells me how many twos are in the number, and so on until the tenth digit which tells me how many nines are in the number. What is my number?

Also, the solution video.

21 January 2016 Edit: 20 January 2016