Still More "So What?"

[soroban]

This sentence contains:
. . forty-one words
. . . . (A hyphenated word is one word -
. . . . seventeen nouns,
. . . . two verbs,
. . . . nineteen adjectives,
. . . . one preposition,
. . . . and two conjunctions),
. . eleven commas,
. . two hyphens,
. . one colon,
. . one dash,
. . one pair of parentheses,
. . two hundred twenty-four letters,
. . and one period.

 

[MarkFL]

I feel I must say:

So What?

 

[Evgeny.Makarov]

So What?

Here's what.

There exists at least one ten digit number where the first digit is the number of times a zero appears in the number. The second digit is the number of times a one appears in the number. The third digit is the number of times a two appears in the number. This pattern continues until the last digit is the number of times a nine appears in the number. Can you find such a number? How many such numbers are there? Explain why.

This puzzle was published in the New York Times, though it is probably a folklore. I read it much earlier, if I remember correctly, in a newsletter by the Association for Logic Programming.

 

[MarkFL]

I believe I have found the only solution:

Spoiler

6210001000