The correct option is C 18, 1
Core electrons are the electrons which are in the completely filled shells.
Valence electrons are the electrons which are present in shells which are not completely filled. These electrons are added to the shell with highest principle quantum number (with exceptions) and has highest energy level.
Electronic configuration of K is 1s22s22p63s23p64s1
So, number of core electrons are 18 as they have been completely filled shells.
Number of valence electrons = 1