Question 1018796
C(18,3) = 816 is the number of ways of selecting any three books from the eighteen books without any restriction.
Now the number of ways in which one book of each color is selected is 210, which you have correctly determined.  The complement of this event is the event in which AT LEAST one book of some color is selected.
Thus, the number of ways in which a selection includes more than one color is 
816 - 210 = 606.