1. ## Combinatorics

I'm stumped on this recreational problem:

How many 5-digit numbers are there such that every next digit is smaller than the previous one?

2. Originally Posted by elninio
I'm stumped on this recreational problem:

How many 5-digit numbers are there such that every next digit is smaller than the previous one?
$\binom{10}{5}$

3. Hmm, I didnt think it would be that simple!

4. Originally Posted by elninio
Hmm, I didnt think it would be that simple!
Well give me any subset of five digits.
Say $\{3,9,0,7,4\}$.
Arrange is desending order: $97430$.
That's sort of number described.
So it is just the number of five element subsets of the digits.