計算機數學

Using the setup from problem 16 (let $X = \{1,2,3,4,5,6\}$ and $Y = \{a,b,c,d\}$; $f(S) = \{f(i) \mid i \in S\}$).

(4分) How many functions $f: X \to Y$ are there such that $|f(X)| = 3$?