- #1

- 307

- 0

## Homework Statement

Compute how many n-digit numbers can be made from the digits of at least one of {0,1,2,3,4,5,6,7,8,9 }

Assume, repetition or order do not matter.

## Homework Equations

## a_{1}, a_{2}, ..., a_{n} ##

## The Attempt at a Solution

10 choices for the 1st sub-index, 10 choices for the second sub-index, ..., 10 choices for the nth- sub-index.

## 10^{n} ## total possible combinations.

I think that now we need to add 'n' for a set full of one identical digit. i.e.: {2,2,...,n-th}

Now, n*9 for all possibilities

Now, I need to take some n_i number into account in pairs and each of the n-2 numbers repeated for each number.

So, groups of two repeated for each i-th number?

Also, then I would extend this to include triple identical numbers and the rest (n-3) numbers in the set?

And, so on...?

I am sorry, if this does not make any sense or it is too messy.

Could someone give me any guidance?

Thank you.