If m=n find # of functions A onto B is m!. Using the string approach, would that be a satisfactory way of proving it to all sets with m=n? What do you think??
for ex)
input:__a(1) a(2)...___a(m)
choices:a(m) a(m-1)....a(1)= a(m)*a(m-1)*...*a(1)=m!
I don't know what the "string approach" is either, unless you mean "stringing together prior probability inverses to get the total probability" which seems to be what you're doing.
Also, please say finite set. This formula is not true in the general case (there are models of ZFC where although , (despite the fact it should be the correct answer in this case).