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Anyway, so i was hoping someone could maybe derive or at least explain binomial coefficients. Like, i know that binomial(n,r)= n!/(n-r)!r! but why? in class the guy was explaining something like, if you're counting, and you're trying to arrange 3 balls into 2 groups then its like...

|1 2 3

1|2 3

1 2|3

1 2 3|

and that because of that, it was like, the formula we'd use for this problem would be binomial(n+r-1, r-1), and then we plug that into the factorial problem... and voila... but, i dunno. this didn't make sense to me at all. we introduce a divider, and we derive some formula for it... and... eh...

so, i see how the method was convienient, but i think there must be some more formal way of going about it. soo...