How many one-to-one correspondences exist between two sets with

Question

A) 8 elements each?

B) n-1 elements each?

Answer 1

Do you mean how many separate pairings exist between two groups of objects, each of which contains eight elements? If so, the answer is (8 x 8) = 64.

The reason I'm slightly cautious about the answer is that I'd have expected the second part of the question to be asking the same about n elements each as opposed to (n-1), unless this is leading up to a simple demonstration of mathematical induction, i.e. demonstrate the answer for n=1, then prove that if it's true for (n-1) then it must be true for n.