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?

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- Dec 13th 2009, 03:49 AMjmedsy[SOLVED] number of onto functions
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? - Dec 13th 2009, 04:22 AMShanks
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 .