But this is not the correct answer to our counting problem, because one of these functions is \(f= \twoline{1\amp 2\amp 3}{a\amp a\amp a}\text{;}\) one friend can get more than one game. What we really need to do is count injective functions. This gives \(P(5,3) = 60\) functions, which is the answer to our counting question.
in-context