sets

[andrian]

The number of partitions of {1,2,3,4,5} into three blocks is S(5,3) = 25. The total number of functions f : {1, 2, 3, 4, 5} → {1, 2, 3, 4} with |Image(f)| = 3 is
 
(a)      4x6
(b)      4 x 25
(c)      25 x 6
(d)      4 x 25 x 6
(e)      3 x 25 x 6