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We started to study all this subject of combinatorics integrated with the subject of functions.

1. I don't actually understand how to integrate between combinatorics and function, those functions which represent our possibilities and etc...

And why at all we need to represent our combinatoric problem with an answer integrating functions?

2. Secondly, we get this formula to calculate some sorts of possibilities:

$\frac {n!} {(n-k)!}$

It's not clear to me why is this really correct, what is posed behind it?

3. For the Newton's binom - the lecturer has presented the proof for it but I don't understand it well, he also used the formula from above (2) to present the proof.

Thank you!