We will find how many numbers contain no ones:

There are 9 choices of numbers for the first digit: 0,2,3,4,5,6,7,8,9

Simarly there are 9 choices for the second, third, fourth, fifth,and sixth digits.

Applying the fundamental counting theorem there are 9x9x9x9x9x9 different numbers with no ones ; `9^6=531441` .

We can use the fundamental counting theorem to find the total number of 6 digit numbers: 10x10x10x10x10x10-1 (000000 is not allowed). So there are `10^6-1=999999` different numbers.

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There are 999999-531441=468558 different numbers with at least one 1 in them.

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