1. ## Subsets

This is my question, i can do the first part but then i need help with the rest please.

How many ordered 5-subsets of {0,...,9} are there? How many of these start with 0? How many positive integers of exactly 5 digits, but with no two digits the same, are there? (In base 10.)

2. ## Re: Subsets

Originally Posted by jonnyl
How many ordered 5-subsets of {0,...,9} are there? How many of these start with 0? How many positive integers of exactly 5 digits, but with no two digits the same, are there? (In base 10.)
These are permutations: $_NP_k=\frac{N!}{(N-k)!}$

3. ## Re: Subsets

So how would i use this to do the rest of the question?

4. ## Re: Subsets

Originally Posted by jonnyl
So how would i use this to do the rest of the question?
You should show some effort here.
What answer do you get for the first part?

5. ## Re: Subsets

I got 30240 for the first part, then 3024 for the second. But i dont really know how to do the last bit

6. ## Re: Subsets

Originally Posted by jonnyl
I got 30240 for the first part, then 3024 for the second. But i dont really know how to do the last bit
Those are correct.

7. ## Re: Subsets

so how would i go about doing the last part?

8. ## Re: Subsets

Originally Posted by jonnyl
so how would i go about doing the last part?
It depends on how one understands the question.
We all know that 70412 is a five digit number with all digits different.
But would 09876 also count? It is five digits all of which are different.
If we do not allow a leading zero then the answer is:
$_{10}P_5 -~_9P_4$.

9. ## Re: Subsets

But surely _{10}P_5-~_9P_4 is inclusive of numbers with repeated digits?

10. ## Re: Subsets

Originally Posted by jonnyl
But surely _{10}P_5-~_9P_4 is inclusive of numbers with repeated digits?
No, it most certainly does not.
If you do that calculation, you will see the result is just the answer in part 1 minus the answer in part 2.