In a class of 12 students, there are 3 girls. The number of different ways, in which they can be arranged in a row such that no two girls are consecutive, are

The 9 boys may occupy 9 places in ⁹P₉ = 9! = 362880 ways. Since no two girls are to sit together, we may arrange the 3 girls at the 10 places shown by x marks as below:

        XBXBXBXBXBXBXBXBXBX

 

Now, the 3 girls at 10 places may be seated in:

¹⁰P₃ = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 604800 ways

 

Therefore, the required number of ways = (362880 x 604800) = 219469824000 ways.