In how many ways can 9 balls of which 4 are red, 4 are white and 1 black be arranged in a line so that no red ball is next to the black?
Case 1: 1st ball is black in the whole row of 9 balls
Case 2: last ball is black
Case 3: Black ball is not the 1st or last ball
Using the addition principle, total number of ways = 35+35+105= 175