  There is no trivial mathematics, there are only trivial mathematicians! A
mathematician is trivial if he or she believes that there exists trivial
mathematics. Being a non-trivial mathematician myself, I will describe ten
different proofs of the seemingly trivial fact that the number of ways of
choosing k people out of n people is less than or equal to the number of ways
of choosing k+1 people out of n people, provided that k is less than half of n.
