a digit k is called nice if there are exactly k digits k in the number. How many 8 digit numbers.are there so that all their digits are nice and no digit is smaller than any other digit to the left of it?

Can you give an example of your 8-digit "k nice" number?

12345678

12233344 that is no good so it can't have 1 2 AND 3

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13334444 that works

12255555 that works

33355555

22666666

17777777

88888888

That is it. There are 6 of them.