Ok, so suppose I have a Domain set A with 5 elements {1,2,3,4,5} that maps to CoDomain set B with 3 elements {A,B,C}
How do I find how many surjective functions there are?
My intuition was to take all the functions: 3^5 and subtract it from
functions of range 2 (only map to 2 elements): 3(2^5)
functions of range 1 (only map to 1 element): 1
To equal 3^5-((3*2^5)+1)
all the solutions i've seen online seem to not take into account for range 1, I'm just wondering why