How many onto functions are there from a set with n elements to a set with three elements?
Could somebody explain how to do this, perhaps substituting 5 in for n?
You can solve it by recusive definition: suppose
Let be the number of onto function from a set with n elements to a set with three elements, be the number of onto function from a set with n elements to a set with two elements.
then what is the recusive relation between , and ?
while it is easy to see that .