This doesn't make sense...

Shouldn't it be marked out that it's everything minus 5 choose 2 because just 5 choose 2 is not equal to 5 choose 3?Also the entire explanation doesn't make sense help what is Prof. Loh trying to do here?

Oh wait 5 choose 3 is equal to 5 choose 2 I just found out weird...

@TheBladeDancer It's great that you noticed this! Yes, you can see from the diagram below that for every way there is to choose two spots, it's equivalent to a way that chooses three spots (the three spots that you don't take).
There are \(10\) ways, and both \(\binom{5}{3} \) and \(\binom{5}{2} \) equal \(10.\)
This is such a cool concept, and you'll see later on in this course the magical symmetry of Pascal's Triangle that lies beneath this general fact that \( \binom{n}{m} = \binom{n}{nm}.\)

@debbie
It's like choosing 3 children to go to a maths competition out of 5 is the same as choosing 2 children to not go to the maths competition out of the same 5.