How many 6 digit numbers are there in all?

Chapter/Topic: Surface Areas and Volumes

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900000

600000

500000

300000

answer is A.

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Detailed Solution

We are asked to find the number of 6 digit numbers that are there in total.
Let us assume that there are 6 boxes that represent the 6 places of a 6 digit number as follows
Now, let us take the number of possibilities for the first box.
We know that there are 10 digits from 0 to 9
But we know that the first place should not be 0 because if the first place occupies 0 then it becomes 5 digit number
So, we get the number of possibilities for first box as 9 by excluding the 0
Now, by taking the number of possibilities for first box then we get
Here, we can see that we need all 6 digit numbers which means that the digits can be repeated
So, we can say that all the remaining boxes have possibilities of 10 digits as the digits can be repeated.
By taking the number of possibilities in other boxes then we get
Now, let us assume that the total number of 6 digit numbers as N
We know that the total number of numbers is the permutations of each box’s possibility
By using the above condition we get the total number of 6 digit numbers as
9 x10 x10 x10 x10 x10=900000
Hence, Option (1) is the correct answer.

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