How many combinations of 6-digit number between 000001 to 999999 that contains the digit 1 or multiples of digit 1? The 6 digit number is between 000001 to 999,999. The combinations must contain at least 1 digit of "1" or multiples of digit "1" such as 000010, 013141, 001268, 161113, etc
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You are watching: How many possible combinations of 6 numbers 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` .

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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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