Given a fair dice with $10$ sides numbered $1$ through to $10$, I roll the dice $5$ times, what is the probability that each successive number is strictly increasing.
I really don't even know where to start. Could someone explain how this could be done.
I'm stuck on, since I can't count them, how I can split the problem up as, you can start with values of 1 to 6, then 2 to 7, but you can't have 2 if you have 6, so I dont know how to get around that
Hint: The set of sequences of length $5$ which are strictly increasing and whose entries are all natural numbers between $1$ and $10$ are in direct bijection with the set of size-$5$ subsets of $\{1,2,3,\dots,10\}$.
For example, the sequence $1,~2,~7,~8,~9$ corresponds to the subset $\{1,2,7,8,9\}$