Kid have 8 black balls and 8white balls. He is trying to arrange a ball in a row then in how many ways can he arrange these balls in a row so that balls of different colors alternate? Choices.
A) (8!)^2 B) 2×(8!) C) 2×(8!)^2 D) 2^2 E) 3×(6!)^2
8 black balls can be arranged in 8! ways ...(A)   Now we need to arrange white balls such that white balls and black balls are positioned alternatively. i.e., we can arrange 8 white balls either in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I as shown below.   8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H in 8! ways.   8 white balls can be arranged in the 8 positions marked as B,C,D,E,F,G,H,I in 8! ways.   8 white balls can be arranged in the 8 positions marked as A,B,2×(8!)^2,D,E,F,G,H or in the 8 positions marked as B,2×(8!)^2,D,E,F,G,H,I in 8!+8!=2×8! ways ...(B)   From (A) and (B),   required number of ways =8!×2×8!=2×(8!)^2   2×(8!)^2
<result>C</result>
Kid have 8 black balls and 8white balls. He is trying to arrange a ball in a row then in how many ways can he arrange these balls in a row so that balls of different colors alternate?