Find the number of ways of arrangement 6 red balls and 6 black balls in a row such that no two black ball are together.

Step-by-step solution

Number of ways to arrange 6 red balls are 6 !. Now, there are seven positions to place 6 black balls, such that no two black balls are together So, number of ways to arrange 6 black balls are ^7 P₆ . Therefore the required number of arrangements =6 ! ^7 P₆=6 ! 7 !=7 6 ! 6 !