Kiran has 8 black balls and 8 white balls. In how many ways can he arrange these balls in a row so that balls of different colours are alternate?

• The 8 black balls can be arranged in
  8P8 = 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
  
  Explanation to Problem on Permutation
  
  8 white balls can be arranged in the 8 positions
  marked as A,B,C,D,E,F,G,H in 8P8 = 8! Ways
  
  8 white balls can be arranged in the 8 positions
  marked as B,C,D,E,F,G,H,I in 8P8 = 8! Ways
  
  8 white balls can be arranged 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
  in 8! + 8! = 2 × 8! Ways ---(B)
  
  From (A) and (B),
  the required number of ways = 8! × 2 × 8! = 2 × (8!)2
• 5 years agoHelpfull: Yes(0) No(0)