Let A = {1,3,5,7,9} and B = {2,4,6,8,10}. Let f be a randomly chosen
function from the set A ∪ B into itself. There are relatively prime positive
integers m and n such that m is the probability that f is a one-to-one function n
on A∪B given that it maps A one-to-one into A∪B and it maps B one-to-one into A ∪ B. Find m + n.

Question

Let A = {1,3,5,7,9} and B = {2,4,6,8,10}. Let f be a randomly chosen
function from the set A ∪ B into itself. There are relatively prime positive
integers m and n such that m is the probability that f is a one-to-one function n
on A∪B given that it maps A one-to-one into A∪B and it maps B one-to-one into A ∪ B. Find m + n.

anonymous · Answer

Where are you stuck? what have you done so far?

anonymous · Answer

I don't even KNOW where to start... What's your thought process?