Concept
Why are the binomial coefficients symmetric?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Now in some ways we’re on a bit of a tangent, since the fact that the “n-choose-k” values happen to work out to be the same as the binomial coefficients is mostly just an interesting coincidence. But what I really want you to take notice of here — and what Pascal’s triangle makes plain — is the symmetry of the coefficients. This surprises a lot of students. What if I asked you which of the following numbers was greater: ( 1000 18 ) or ( 1000 982 ) ? Most students guess that the second of these numbers is far greater. In actual fact, though, they both work out to be 1000! 18!982! and are thus exactly the same."
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