The number of surjections (onto functions) from a set of N elements to a set of M is given by:
of course .
So 5796 is correct.
Please confirm I'm doing this correctly:
How many onto functions are there from a set with eight elements to a set with 3 elements?
Steps
1. There are functions total.
2. There are 3 functions with 1 element in range.
3. There are functions with 2 elements in the range for each pair of elements in the codomain.
4. There are "3 choose 2"=3 ways to choose 2 elements from a set of 3.
5. Considering steps 1. through 4., the number of onto functions is:
onto functions
I'm almost positive this is correct. Could somebody please confirm?