The title may be a little misleading. Let's say we choose 5 out of 60 balls. We write down the result which are in a form as $k_1,k_2,k_3,k_4,k_5$.
I have to calculate the probability of this happening :
\begin{aligned}k_1<k_2<k_3<k_4<k_5\end{aligned}
Also, the probability of this happening:
\begin{aligned}k_1>\max\{k_2,k_3,k_4,k_5\}\end{aligned}
We do care for the order so the number of the elements in the sample space is : $$\frac{60!}{(60-5)!}$$ I am stuck there. I can't think of anything to do to calculate those two probabilities. I would appreciate it if someone could help me. Thanks in advance!