# 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...

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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### 2 Answers

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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if an analog machine ranging from 000001-999999 is spanned 5 times and the result of the first spin is 403849,of second spin 968892,of third spin 249376,of fourth spin 007251 and of fifth spin is 420462 respectively then what will be the result of the the next spin?