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 $k\_1,k\_2,k\_3,k\_4,k\_5$. 

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> I have to calculate the probability of this happening :
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\begin{aligned}k\_1<k\_2<k\_3<k\_4<k\_5\end{aligned}

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> Also, the probability of this happening:
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\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!