(a) Let \(S=\{1,2,3\}\) and \(T=\{1,2,3,4,5\}\). How many functions are there from \(S\) to \(T\) ? How many of these are 1-1?

(b) Let \(|S|=m,|T|=n\) with \(m \leq n\). Show that the number of 1-1 functions from \(S\) to \(T\) is equal to \(n(n-1)(n-2) \cdots(n-m+1)\).

Give formulae describing the functions \(g \circ f\) and \(f \circ g\). Draw the graphs of these functions.